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A Study of $\phi$-Pluriharmonicity in Quasi bi-slant Conformal $\xi^\perp$-Submersions From Kenmotsu Manifold

Year 2024, , 317 - 335, 27.10.2024

Ibrahim Al-dayel , Mohammad Shuaib , Tanveer Fatima , Fahad Sikander

https://doi.org/10.36890/iejg.1312986

Abstract

In the present research paper, we look into quasi bi-slant conformal $\xi^{\perp}$-submersions from Kenmotsu manifolds onto Riemannian manifolds as a generalisation of quasi hemi-slant conformal submersions. We investigate the geometry of distributions's leaves in order to explain integrability conditions for distributions. Furthermore, we study of certain decomposition theorems, additionaly provide non-trivial examples of quasi bi-slant conformal $\xi^{\perp}$-submersions from Kenmotsu manifolds. We also look at the $\phi$-pluriharmonicity of quasi bi-slant conformal $\xi^{\perp}$-submersions.

Keywords

Kenmotsu manifold Riemannian submersions bi-slant submersions quasi bi-slant submersions

Supporting Institution

The Deanship of Scientific research, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia,

Project Number

(221412008)

References

  • [1] Akyol, M. A., Gunduzalp, Y.: Hemi-slant submersions from almost product Riemannian manifolds. Gulf J. Math. 4 (3), 15-27 (2016).
  • [2] Akyol, M. A.: Conformal semi-slant submersions. International Journal of Geometric Methods in Modern Physics. 14 (7) 1750114 (2017).
  • [3] Akyol, M. A., Sahin, B.: Conformal slant submersions. Hacettepe Journal of Mathematics and Statistics. 48 (1) 28-44 (2019).
  • [4] Akyol, M. A., Sahin, B.: Conformal anti-invariant submersions from almost Hermitian manifolds. Turkish Journal of Mathematics. 40 43-70 (2016).
  • [5] Akyol, M. A., Sahin, B.: Conformal semi-invariant submersions. Communications in Contemporary Mathematics. 19 1650011 (2017).
  • [6] P. Baird and J. C. Wood., Harmonic Morphisms Between Riemannian Manifolds, London Mathematical Society Monographs, 29, Oxford University Press, The Clarendon Press. Oxford, (2003).
  • [7] Bourguignon, J. P., Lawson, H. B. Jr.: Stability and isolation phenomena for Yang Mills fields. Comm. Math. Phys. 79 2 189-230 (1981). http://projecteuclid. org/euclid.cmp/1103908963.
  • [8] Chinea, D.: Almost contact metric submersions Rend. Circ. Mat. Palermo. 34 (1) 89-104 (1985).
  • [9] Cabrerizo, J. L., Carriazo, A., Fernandez, L. M., Fernandez, M.: Slant submanifolds in Sasakian manifolds. Glasg. Math. J. 42 (1) 125-138 (2000).
  • [10] Erken, I. K., Murathan, C.: On slant Riemannian submersions for cosymplectic manifolds. Bull. Korean Math. Soc. 51 (6) 1749-1771 (2014).
  • [11] Falcitelli, M., Ianus, S., Pastore, A. M.: Riemannian submersions and Related Topics. World Scientific, River Edge, NJ. (2004).
  • [12] Gray, A.: Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16 715-737 (1967).
  • [13] Fuglede, B.: Harmonic morphisms between Riemannian manifolds. Annales de l’institut Fourier (Grenoble). 28 107-144 (1978).
  • [14] Gudmundsson, S.: The geometry of harmonic morphisms. Ph.D. thesis, University of Leeds. (1992).
  • [15] Gudmundsson, S., Wood, J. C.: Harmonic morphisms between almost Hermitian manifolds. Boll. Un. Mat. Ital. B 7 11 no. 2 185-197 (1997).
  • [16] Gunduzalp, Y.: Semi-slant submersions from almost product Riemannian manifolds. Demonstratio Mathematica. 49 (3)345-356 (2016).
  • [17] Gunduzalp, Y., Akyol, M.A.: Conformal slant submersions from cosymplectic manifolds. Turkish Journal of Mathematics. 48 2672-2689 (2018).
  • [18] Ianuş, S., Vi¸sinescu, M.: Space-time compaction and Riemannian submersions. In: Rassias, G.(ed.) The Mathematical Heritage of C. F. Gauss, World Scientific, River Edge. 358-371 (1991).
  • [19] Ianuş, S., Vi¸sinescu, M.: Kaluza-Klein theory with scalar fields and generalised Hopf manifolds. Classical Quantum Gravity. 4 no. 5, 1317–1325 (1987). http://stacks.iop.org/0264-9381/4/ 1317.
  • [20] Ishihara, T.: A mapping of Riemannian manifolds which preserves harmonic functions. Journal of Mathematics of Kyoto University. 19 215-229 (1979).
  • [21] Kenmotsu, K.: A class of almost contact Riemannian manifolds. Tohoku Math. 24 93-103 (1972).
  • [22] Mustafa, M. T.: Applications of harmonic morphisms to gravity. J. Math. Phys. 41 6918-6929 (2000).
  • [23] Noyan, E. B., Gunduzalp, Y.: Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry. International Electronic Journal of Geometry 15 NO. 2, 253–265 (2022). DOI: HTTPS://DOI.ORG/10.36890/IEJG.1033345
  • [24] Noyan, E. B., Gunduzalp, Y.: Proper bi-slant Pseudo Riemannian Submersions whose total manifolds are Para-Kaehler manifolds. Honam Mathematical J. 44, No. 3 370–383 (2022). https://doi.org/10.5831/HMJ.2022.44.3.370
  • [25] Ohnita, Y.: On pluriharmonicity of stable harmonic maps. J. London Math. Soc. 2 2 563-568 2.2 (1987).
  • [26] O’Neill, B.: The fundamental equations of a submersion. Michigan Math. J. 13 459–469 (1966). http://projecteuclid.org/euclid.mmj/1028999604.
  • [27] Park, K. S., Prasad, R.: Semi-slant submersions. Bull. Korean Math. Soc. 50 (3) 951-962 (2013).
  • [28] Prasad, R., Shukla, S. S., Kumar, S.: On Quasi bi-slant submersions. Mediterr. J. Math. 16 (2019). https://doi.org/10.1007/s00009-019-1434-7.
  • [29] Prasad, R., Akyol, M. A., Singh, P. K., Kumar, S.: On Quasi bi-slant submersions from Kenmotsu manifolds onto any Riemannian manifolds. Journal of Mathematical Extension. 8 (16) (2021).
  • [30] Prasad, R., Kumar, S.: Conformal anti-invariant submersions from nearly Kaehler Manifolds. Palestine Journal of Mathematics. 8 (2) (2019).
  • [31] Ponge, R., Reckziegel, H.: Twisted products in pseudo-Riemannian geometry. Geom. Dedicata. (1993), 48 (1) 15-25 (1993).
  • [32] Tanno, S.: The automorphism groups of almost contact metric manfolds. Tohoku Math., J. 21 21-38 (1969).
  • [33] Sahin, B.: Anti-invariant Riemannian submersions from almost Hermitian manifolds. Central European J. Math. 3 437-447 (2010).
  • [34] Sahin, B.: Semi-invariant Riemannian submersions from almost Hermitian manifolds. Canad. Math. Bull. 56 173-183 (2013).
  • [35] Sahin, B.: Slant submersions from almost Hermitian manifolds. Bull. Math. Soc. Sci. Math. Roumanie. 1 93-105 (2011).
  • [36] Sahin, B. and Akyol, M. A.: Conformal Anti-Invariant Submersion From Almost Hermitian Manifolds. Turk J Math 40, 43 – 70(2016).
  • [37] Shuaib, M., Fatima, T.: A note on conformal hemi-slant submersions. Afr. Mat. 34 4 (2023).
  • [38] Sumeet Kumar et al.: Conformal hemi-slant submersions from almost hermitian manifolds. Commun. Korean Math. Soc. 35 no. 3 999-1018 (2020). https://doi.org/10.4134/CKMS.c190448 pISSN: 1225-1763 / eISSN: 2234-3024.
  • [39] Tastan, H. M., S¸ahin, B., Yanan, S.: Hemi-slant submersions, Mediterr. J. Math. 13 (4), 2171-2184 (2016).
  • [40] Watson, B.: Almost Hermitian submersions. J. Differential Geometry. 11 no. 1, 147-165 (1976).
  • [41] Watson, B.: G, G’-Riemannian submersions and nonlinear gauge field equations of general relativity. In: Rassias, T. (ed.) Global Analysis - Analysis on manifolds, dedicated M. Morse. Teubner-Texte Math., 57 324-349 (1983), Teubner, Leipzig

Year 2024, , 317 - 335, 27.10.2024

Ibrahim Al-dayel , Mohammad Shuaib , Tanveer Fatima , Fahad Sikander

https://doi.org/10.36890/iejg.1312986

Abstract

Project Number

(221412008)

References

  • [1] Akyol, M. A., Gunduzalp, Y.: Hemi-slant submersions from almost product Riemannian manifolds. Gulf J. Math. 4 (3), 15-27 (2016).
  • [2] Akyol, M. A.: Conformal semi-slant submersions. International Journal of Geometric Methods in Modern Physics. 14 (7) 1750114 (2017).
  • [3] Akyol, M. A., Sahin, B.: Conformal slant submersions. Hacettepe Journal of Mathematics and Statistics. 48 (1) 28-44 (2019).
  • [4] Akyol, M. A., Sahin, B.: Conformal anti-invariant submersions from almost Hermitian manifolds. Turkish Journal of Mathematics. 40 43-70 (2016).
  • [5] Akyol, M. A., Sahin, B.: Conformal semi-invariant submersions. Communications in Contemporary Mathematics. 19 1650011 (2017).
  • [6] P. Baird and J. C. Wood., Harmonic Morphisms Between Riemannian Manifolds, London Mathematical Society Monographs, 29, Oxford University Press, The Clarendon Press. Oxford, (2003).
  • [7] Bourguignon, J. P., Lawson, H. B. Jr.: Stability and isolation phenomena for Yang Mills fields. Comm. Math. Phys. 79 2 189-230 (1981). http://projecteuclid. org/euclid.cmp/1103908963.
  • [8] Chinea, D.: Almost contact metric submersions Rend. Circ. Mat. Palermo. 34 (1) 89-104 (1985).
  • [9] Cabrerizo, J. L., Carriazo, A., Fernandez, L. M., Fernandez, M.: Slant submanifolds in Sasakian manifolds. Glasg. Math. J. 42 (1) 125-138 (2000).
  • [10] Erken, I. K., Murathan, C.: On slant Riemannian submersions for cosymplectic manifolds. Bull. Korean Math. Soc. 51 (6) 1749-1771 (2014).
  • [11] Falcitelli, M., Ianus, S., Pastore, A. M.: Riemannian submersions and Related Topics. World Scientific, River Edge, NJ. (2004).
  • [12] Gray, A.: Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16 715-737 (1967).
  • [13] Fuglede, B.: Harmonic morphisms between Riemannian manifolds. Annales de l’institut Fourier (Grenoble). 28 107-144 (1978).
  • [14] Gudmundsson, S.: The geometry of harmonic morphisms. Ph.D. thesis, University of Leeds. (1992).
  • [15] Gudmundsson, S., Wood, J. C.: Harmonic morphisms between almost Hermitian manifolds. Boll. Un. Mat. Ital. B 7 11 no. 2 185-197 (1997).
  • [16] Gunduzalp, Y.: Semi-slant submersions from almost product Riemannian manifolds. Demonstratio Mathematica. 49 (3)345-356 (2016).
  • [17] Gunduzalp, Y., Akyol, M.A.: Conformal slant submersions from cosymplectic manifolds. Turkish Journal of Mathematics. 48 2672-2689 (2018).
  • [18] Ianuş, S., Vi¸sinescu, M.: Space-time compaction and Riemannian submersions. In: Rassias, G.(ed.) The Mathematical Heritage of C. F. Gauss, World Scientific, River Edge. 358-371 (1991).
  • [19] Ianuş, S., Vi¸sinescu, M.: Kaluza-Klein theory with scalar fields and generalised Hopf manifolds. Classical Quantum Gravity. 4 no. 5, 1317–1325 (1987). http://stacks.iop.org/0264-9381/4/ 1317.
  • [20] Ishihara, T.: A mapping of Riemannian manifolds which preserves harmonic functions. Journal of Mathematics of Kyoto University. 19 215-229 (1979).
  • [21] Kenmotsu, K.: A class of almost contact Riemannian manifolds. Tohoku Math. 24 93-103 (1972).
  • [22] Mustafa, M. T.: Applications of harmonic morphisms to gravity. J. Math. Phys. 41 6918-6929 (2000).
  • [23] Noyan, E. B., Gunduzalp, Y.: Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry. International Electronic Journal of Geometry 15 NO. 2, 253–265 (2022). DOI: HTTPS://DOI.ORG/10.36890/IEJG.1033345
  • [24] Noyan, E. B., Gunduzalp, Y.: Proper bi-slant Pseudo Riemannian Submersions whose total manifolds are Para-Kaehler manifolds. Honam Mathematical J. 44, No. 3 370–383 (2022). https://doi.org/10.5831/HMJ.2022.44.3.370
  • [25] Ohnita, Y.: On pluriharmonicity of stable harmonic maps. J. London Math. Soc. 2 2 563-568 2.2 (1987).
  • [26] O’Neill, B.: The fundamental equations of a submersion. Michigan Math. J. 13 459–469 (1966). http://projecteuclid.org/euclid.mmj/1028999604.
  • [27] Park, K. S., Prasad, R.: Semi-slant submersions. Bull. Korean Math. Soc. 50 (3) 951-962 (2013).
  • [28] Prasad, R., Shukla, S. S., Kumar, S.: On Quasi bi-slant submersions. Mediterr. J. Math. 16 (2019). https://doi.org/10.1007/s00009-019-1434-7.
  • [29] Prasad, R., Akyol, M. A., Singh, P. K., Kumar, S.: On Quasi bi-slant submersions from Kenmotsu manifolds onto any Riemannian manifolds. Journal of Mathematical Extension. 8 (16) (2021).
  • [30] Prasad, R., Kumar, S.: Conformal anti-invariant submersions from nearly Kaehler Manifolds. Palestine Journal of Mathematics. 8 (2) (2019).
  • [31] Ponge, R., Reckziegel, H.: Twisted products in pseudo-Riemannian geometry. Geom. Dedicata. (1993), 48 (1) 15-25 (1993).
  • [32] Tanno, S.: The automorphism groups of almost contact metric manfolds. Tohoku Math., J. 21 21-38 (1969).
  • [33] Sahin, B.: Anti-invariant Riemannian submersions from almost Hermitian manifolds. Central European J. Math. 3 437-447 (2010).
  • [34] Sahin, B.: Semi-invariant Riemannian submersions from almost Hermitian manifolds. Canad. Math. Bull. 56 173-183 (2013).
  • [35] Sahin, B.: Slant submersions from almost Hermitian manifolds. Bull. Math. Soc. Sci. Math. Roumanie. 1 93-105 (2011).
  • [36] Sahin, B. and Akyol, M. A.: Conformal Anti-Invariant Submersion From Almost Hermitian Manifolds. Turk J Math 40, 43 – 70(2016).
  • [37] Shuaib, M., Fatima, T.: A note on conformal hemi-slant submersions. Afr. Mat. 34 4 (2023).
  • [38] Sumeet Kumar et al.: Conformal hemi-slant submersions from almost hermitian manifolds. Commun. Korean Math. Soc. 35 no. 3 999-1018 (2020). https://doi.org/10.4134/CKMS.c190448 pISSN: 1225-1763 / eISSN: 2234-3024.
  • [39] Tastan, H. M., S¸ahin, B., Yanan, S.: Hemi-slant submersions, Mediterr. J. Math. 13 (4), 2171-2184 (2016).
  • [40] Watson, B.: Almost Hermitian submersions. J. Differential Geometry. 11 no. 1, 147-165 (1976).
  • [41] Watson, B.: G, G’-Riemannian submersions and nonlinear gauge field equations of general relativity. In: Rassias, T. (ed.) Global Analysis - Analysis on manifolds, dedicated M. Morse. Teubner-Texte Math., 57 324-349 (1983), Teubner, Leipzig
There are 41 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Ibrahim Al-dayel 0000-0002-5901-2511

Mohammad Shuaib 0000-0003-0022-893X

Tanveer Fatima 0000-0001-9905-2107

Fahad Sikander 0000-0001-6560-8525

Project Number (221412008)
Early Pub Date September 16, 2024
Publication Date October 27, 2024
Acceptance Date November 2, 2023
Published in Issue Year 2024

Cite

APA Al-dayel, I., Shuaib, M., Fatima, T., Sikander, F. (2024). A Study of $\phi$-Pluriharmonicity in Quasi bi-slant Conformal $\xi^\perp$-Submersions From Kenmotsu Manifold. International Electronic Journal of Geometry, 17(2), 317-335. https://doi.org/10.36890/iejg.1312986
AMA Al-dayel I, Shuaib M, Fatima T, Sikander F. A Study of $\phi$-Pluriharmonicity in Quasi bi-slant Conformal $\xi^\perp$-Submersions From Kenmotsu Manifold. Int. Electron. J. Geom. October 2024;17(2):317-335. doi:10.36890/iejg.1312986
Chicago Al-dayel, Ibrahim, Mohammad Shuaib, Tanveer Fatima, and Fahad Sikander. “A Study of $\phi$-Pluriharmonicity in Quasi Bi-Slant Conformal $\xi^\perp$-Submersions From Kenmotsu Manifold”. International Electronic Journal of Geometry 17, no. 2 (October 2024): 317-35. https://doi.org/10.36890/iejg.1312986.
EndNote Al-dayel I, Shuaib M, Fatima T, Sikander F (October 1, 2024) A Study of $\phi$-Pluriharmonicity in Quasi bi-slant Conformal $\xi^\perp$-Submersions From Kenmotsu Manifold. International Electronic Journal of Geometry 17 2 317–335.
IEEE I. Al-dayel, M. Shuaib, T. Fatima, and F. Sikander, “A Study of $\phi$-Pluriharmonicity in Quasi bi-slant Conformal $\xi^\perp$-Submersions From Kenmotsu Manifold”, Int. Electron. J. Geom., vol. 17, no. 2, pp. 317–335, 2024, doi: 10.36890/iejg.1312986.
ISNAD Al-dayel, Ibrahim et al. “A Study of $\phi$-Pluriharmonicity in Quasi Bi-Slant Conformal $\xi^\perp$-Submersions From Kenmotsu Manifold”. International Electronic Journal of Geometry 17/2 (October 2024), 317-335. https://doi.org/10.36890/iejg.1312986.
JAMA Al-dayel I, Shuaib M, Fatima T, Sikander F. A Study of $\phi$-Pluriharmonicity in Quasi bi-slant Conformal $\xi^\perp$-Submersions From Kenmotsu Manifold. Int. Electron. J. Geom. 2024;17:317–335.
MLA Al-dayel, Ibrahim et al. “A Study of $\phi$-Pluriharmonicity in Quasi Bi-Slant Conformal $\xi^\perp$-Submersions From Kenmotsu Manifold”. International Electronic Journal of Geometry, vol. 17, no. 2, 2024, pp. 317-35, doi:10.36890/iejg.1312986.
Vancouver Al-dayel I, Shuaib M, Fatima T, Sikander F. A Study of $\phi$-Pluriharmonicity in Quasi bi-slant Conformal $\xi^\perp$-Submersions From Kenmotsu Manifold. Int. Electron. J. Geom. 2024;17(2):317-35.