Research Article
BibTex RIS Cite

Clairaut Pointwise Slant Submersion from Locally Product Riemannian Manifolds

Year 2023, Volume: 16 Issue: 1, 283 - 294, 30.04.2023
https://doi.org/10.36890/iejg.1108703

Abstract

The goal of the present paper is to analyze some geometric features of Clairaut pointwise slant submersions whose total manifold is a locally product Riemannian manifold. We describe Clairaut pointwise slant submersions from locally product Riemannian manifold onto a Riemannian manifold. We study pointwise slant submersions by providing a consequent which defines the geodesics on the total space of this type submersions. We also give a non-trivial example of the Clairaut pointwise slant submersions whose total manifolds are locally product Riemannian.

References

  • [1] M.A. Akyol, Generic Riemannian submersions from almost product Riemannian manifolds, GUJ Sci. 30, no. 3, 89-100, 2017.
  • [2] M.A. Akyol, Conformal semi-slant submersions, Int. J. Geom. Methods Mod. Phys.14, no.7, 1750114, 2017.
  • [3] S.A. Aykurt and M. Ergut, Pointwise slant submersions from cosymplectic manifolds, Turk. J. Math. 40, no. 3, 582-593, 2016.
  • [4] P. Baird and J.C.Wood, Harmonic morphism between Riemannian manifolds, Oxford science publications, Oxford, 2003.
  • [5] A. Beri, E.I. Kupeli and C. Murathan, Anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds, Turk. J. Math. 40, no. 3, 540-552, 2016.
  • [6] R. L. Bishop, Clairaut submersions, Differential Geometry (in honor of Kentaro Yano), Kinokuniya, Tokyo, 21-31, 1972.
  • [7] B.Y. Chen, geometry of real submanifolds in Kahler manifold, Monatsh. Math., 91, 257-274, 1981.
  • [8] B.Y. Chen and O. Garay, Pointwise slant submanifolds in almost Hermitian manifolds, Turk. J. Math. 364, 630-640, 2012.
  • [9] A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16, 715-737, 1967.
  • [10] Y. Gunduzalp, Anti-invariant Riemannian submersions from almost product Riemannian manifolds, Math. Sci. Appl. E Notes 1, 58-66, 2013.
  • [11] Y. Gündüzalp, Anti-invariant Pseudo-Riemannian Submersions and Clairaut Submersions from Paracosymplectic Manifolds. Mediterr. J. Math. 16, 94, 2019.
  • [12] Y. Gunduzalp, Anti-invariant submersions from almost paracontact Riemannian manifolds, Honam Mathematical Journal, 41(4), 769-780, 2019.
  • [13] Y. Gündüzalp, Slant submersions from almost product Riemannian manifolds, Turkish Journal of Mathematics, 37(5), 863-873, 2013.
  • [14] Y. Gündüzalp and M. Polat, Some inequalities of anti-invariant Riemannian submersions in complex space forms, Miskolc Mathematical Notes, accepted, 2021.
  • [15] Y. Gündüzalp and M. Polat, Chen-Ricci inequalities in slant submersions for complex space forms, F˙ILOMAT, accepted, 2021.
  • [16] I. Kupeli Erken and C. Murathan, On slant submersions for cosymplectic manifolds, Bull. Korean Math. Soc. 51, no. 6, 1749-1771, 2014.
  • [17] J.W. Lee, B. Şahin, Pointwise slant submersions, Bull. Korean Math. Soc. 51, 1115-1126, 2014.
  • [18] J. Lee, J.H. Park, B. Şahin and D.Y. Song, Einstein conditions for the base of anti-invariant Riemannian submersions and Clairaut submersions, Taiwanse J. Math., 19, no. 4, 1145-1160, 2015.
  • [19] B. O‘Neill, The fundamental equations of a submersion, Michigan Math. J. 13, 459-469, 1966.
  • [20] F. ¨ Ozdemir, C. Sayar and H.M. Tas.tan, Semi-invariant submersions whose total manifolds are locally product Riemannian, Quaestiones Mathematicae, Vol. 49 No. 7, 2017.
  • [21] K.S. Park and R. Prasad, Semi-slant submersions, Bull. Korean Math. Soc. 50, no. 3, 951-962, 2013.
  • [22] G.B. Ronsse, Generic and skew CR-submanifolds of a Kahler manifold, Bull. Inst.Math. Acad. Sin. 18, 127-141, 1990.
  • [23] S. A.Sepet and M.Ergut, Pointwise slant submersions from almost product Riemannian manifolds, Journal of Interdisciplinary Mathematics, 23(3) (2020), 639-655.
  • [24] A. Shahid and F. Tanveer, Anti-invariant Riemannian submersions from nearly Kahler manifolds, Filomat, 27, 1219-1235, 2013.
  • [25] A. Shahid and F. Tanveer, Generic Riemannian submersions, Tamkang J. Math. 44, no. 4, 395-409, 2013.
  • [26] B. Sahin, Riemannian submersions, Riemannian maps in Hermitian Geometry, and their Applications, Elsevir, Academic, Amsterdam, 2017.
  • [27] B. Sahin, Semi-invariant submersions from almost Hermitian manifolds, Canad. Math. Bull. 56(1), 173-182, 2013.
  • [28] B. Şahin, Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie Tome 54(102), 93–105, 2011.
  • [29] B. Şahin, Anti-invariant Riemannian submersion from almost Hermitian manifolds, Cent. Eur. J. Math., 8(3) , 437-447, 2010.
  • [30] H.M. Taştan, On Lagrangian submersions, Hacet. J. Math. Stat. 43, no. 6, 993-1000, 2014.
  • [31] H.M. Taştan, B. Sahin and S. Yanan, Hemi-slant submersions, Mediterr. J. Math. 13, no. 4, 2171-2184, 2016.
  • [32] H.M. Taştan, S. Gerdan, Clairaut anti-invariant submersions from Sasakian and Kenmotsu manifolds, Mediterr. J. Math. 14, no. 6, paper no. 235, 17 pp., 2017.
  • [33] H.M. Taştan and S.G. Aydin, Clairaut anti-invariant submersions from cosymplectic manifolds, Honam Math. J. 41, no. 4, 707-724, 2019.
  • [34] K. Yano and M. Kon, Structures on Manifolds, Singapore: World Scientific, 1984.
  • [35] B. Watson, Almost Hermitian submersions, J. Differential Geom. 11, 147-165, 1976.
Year 2023, Volume: 16 Issue: 1, 283 - 294, 30.04.2023
https://doi.org/10.36890/iejg.1108703

Abstract

References

  • [1] M.A. Akyol, Generic Riemannian submersions from almost product Riemannian manifolds, GUJ Sci. 30, no. 3, 89-100, 2017.
  • [2] M.A. Akyol, Conformal semi-slant submersions, Int. J. Geom. Methods Mod. Phys.14, no.7, 1750114, 2017.
  • [3] S.A. Aykurt and M. Ergut, Pointwise slant submersions from cosymplectic manifolds, Turk. J. Math. 40, no. 3, 582-593, 2016.
  • [4] P. Baird and J.C.Wood, Harmonic morphism between Riemannian manifolds, Oxford science publications, Oxford, 2003.
  • [5] A. Beri, E.I. Kupeli and C. Murathan, Anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds, Turk. J. Math. 40, no. 3, 540-552, 2016.
  • [6] R. L. Bishop, Clairaut submersions, Differential Geometry (in honor of Kentaro Yano), Kinokuniya, Tokyo, 21-31, 1972.
  • [7] B.Y. Chen, geometry of real submanifolds in Kahler manifold, Monatsh. Math., 91, 257-274, 1981.
  • [8] B.Y. Chen and O. Garay, Pointwise slant submanifolds in almost Hermitian manifolds, Turk. J. Math. 364, 630-640, 2012.
  • [9] A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16, 715-737, 1967.
  • [10] Y. Gunduzalp, Anti-invariant Riemannian submersions from almost product Riemannian manifolds, Math. Sci. Appl. E Notes 1, 58-66, 2013.
  • [11] Y. Gündüzalp, Anti-invariant Pseudo-Riemannian Submersions and Clairaut Submersions from Paracosymplectic Manifolds. Mediterr. J. Math. 16, 94, 2019.
  • [12] Y. Gunduzalp, Anti-invariant submersions from almost paracontact Riemannian manifolds, Honam Mathematical Journal, 41(4), 769-780, 2019.
  • [13] Y. Gündüzalp, Slant submersions from almost product Riemannian manifolds, Turkish Journal of Mathematics, 37(5), 863-873, 2013.
  • [14] Y. Gündüzalp and M. Polat, Some inequalities of anti-invariant Riemannian submersions in complex space forms, Miskolc Mathematical Notes, accepted, 2021.
  • [15] Y. Gündüzalp and M. Polat, Chen-Ricci inequalities in slant submersions for complex space forms, F˙ILOMAT, accepted, 2021.
  • [16] I. Kupeli Erken and C. Murathan, On slant submersions for cosymplectic manifolds, Bull. Korean Math. Soc. 51, no. 6, 1749-1771, 2014.
  • [17] J.W. Lee, B. Şahin, Pointwise slant submersions, Bull. Korean Math. Soc. 51, 1115-1126, 2014.
  • [18] J. Lee, J.H. Park, B. Şahin and D.Y. Song, Einstein conditions for the base of anti-invariant Riemannian submersions and Clairaut submersions, Taiwanse J. Math., 19, no. 4, 1145-1160, 2015.
  • [19] B. O‘Neill, The fundamental equations of a submersion, Michigan Math. J. 13, 459-469, 1966.
  • [20] F. ¨ Ozdemir, C. Sayar and H.M. Tas.tan, Semi-invariant submersions whose total manifolds are locally product Riemannian, Quaestiones Mathematicae, Vol. 49 No. 7, 2017.
  • [21] K.S. Park and R. Prasad, Semi-slant submersions, Bull. Korean Math. Soc. 50, no. 3, 951-962, 2013.
  • [22] G.B. Ronsse, Generic and skew CR-submanifolds of a Kahler manifold, Bull. Inst.Math. Acad. Sin. 18, 127-141, 1990.
  • [23] S. A.Sepet and M.Ergut, Pointwise slant submersions from almost product Riemannian manifolds, Journal of Interdisciplinary Mathematics, 23(3) (2020), 639-655.
  • [24] A. Shahid and F. Tanveer, Anti-invariant Riemannian submersions from nearly Kahler manifolds, Filomat, 27, 1219-1235, 2013.
  • [25] A. Shahid and F. Tanveer, Generic Riemannian submersions, Tamkang J. Math. 44, no. 4, 395-409, 2013.
  • [26] B. Sahin, Riemannian submersions, Riemannian maps in Hermitian Geometry, and their Applications, Elsevir, Academic, Amsterdam, 2017.
  • [27] B. Sahin, Semi-invariant submersions from almost Hermitian manifolds, Canad. Math. Bull. 56(1), 173-182, 2013.
  • [28] B. Şahin, Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie Tome 54(102), 93–105, 2011.
  • [29] B. Şahin, Anti-invariant Riemannian submersion from almost Hermitian manifolds, Cent. Eur. J. Math., 8(3) , 437-447, 2010.
  • [30] H.M. Taştan, On Lagrangian submersions, Hacet. J. Math. Stat. 43, no. 6, 993-1000, 2014.
  • [31] H.M. Taştan, B. Sahin and S. Yanan, Hemi-slant submersions, Mediterr. J. Math. 13, no. 4, 2171-2184, 2016.
  • [32] H.M. Taştan, S. Gerdan, Clairaut anti-invariant submersions from Sasakian and Kenmotsu manifolds, Mediterr. J. Math. 14, no. 6, paper no. 235, 17 pp., 2017.
  • [33] H.M. Taştan and S.G. Aydin, Clairaut anti-invariant submersions from cosymplectic manifolds, Honam Math. J. 41, no. 4, 707-724, 2019.
  • [34] K. Yano and M. Kon, Structures on Manifolds, Singapore: World Scientific, 1984.
  • [35] B. Watson, Almost Hermitian submersions, J. Differential Geom. 11, 147-165, 1976.
There are 35 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Murat Polat 0000-0003-1846-0817

Publication Date April 30, 2023
Acceptance Date February 15, 2023
Published in Issue Year 2023 Volume: 16 Issue: 1

Cite

APA Polat, M. (2023). Clairaut Pointwise Slant Submersion from Locally Product Riemannian Manifolds. International Electronic Journal of Geometry, 16(1), 283-294. https://doi.org/10.36890/iejg.1108703
AMA Polat M. Clairaut Pointwise Slant Submersion from Locally Product Riemannian Manifolds. Int. Electron. J. Geom. April 2023;16(1):283-294. doi:10.36890/iejg.1108703
Chicago Polat, Murat. “Clairaut Pointwise Slant Submersion from Locally Product Riemannian Manifolds”. International Electronic Journal of Geometry 16, no. 1 (April 2023): 283-94. https://doi.org/10.36890/iejg.1108703.
EndNote Polat M (April 1, 2023) Clairaut Pointwise Slant Submersion from Locally Product Riemannian Manifolds. International Electronic Journal of Geometry 16 1 283–294.
IEEE M. Polat, “Clairaut Pointwise Slant Submersion from Locally Product Riemannian Manifolds”, Int. Electron. J. Geom., vol. 16, no. 1, pp. 283–294, 2023, doi: 10.36890/iejg.1108703.
ISNAD Polat, Murat. “Clairaut Pointwise Slant Submersion from Locally Product Riemannian Manifolds”. International Electronic Journal of Geometry 16/1 (April 2023), 283-294. https://doi.org/10.36890/iejg.1108703.
JAMA Polat M. Clairaut Pointwise Slant Submersion from Locally Product Riemannian Manifolds. Int. Electron. J. Geom. 2023;16:283–294.
MLA Polat, Murat. “Clairaut Pointwise Slant Submersion from Locally Product Riemannian Manifolds”. International Electronic Journal of Geometry, vol. 16, no. 1, 2023, pp. 283-94, doi:10.36890/iejg.1108703.
Vancouver Polat M. Clairaut Pointwise Slant Submersion from Locally Product Riemannian Manifolds. Int. Electron. J. Geom. 2023;16(1):283-94.

Cited By

Clairaut slant Riemannian maps to Kähler manifolds
International Journal of Geometric Methods in Modern Physics
https://doi.org/10.1142/S0219887824501019