Research Article
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Year 2022, Volume: 15 Issue: 2, 253 - 265, 31.10.2022
https://doi.org/10.36890/iejg.1033345

Abstract

References

  • [1] Akyol, M.A., Sarı, R.: On semi-slant $\xi^\bot $ -Riemannian submersions, Preprint arxiv:1704.01412 (2017).
  • [2] Alegre, P., Carriazo, A.: Slant submanifolds of para-Hermitian manifolds. Mediterr. J. Math. 14 (5), 1-14 (2017).
  • [3] Alegre, P., Carriazo, A.: Bi-slant submanifolds of para-Hermitian manifolds. Mathematics. 7 (7), 618 (2019).
  • [4] Baditoiu, G., Ianus, S.: Semi-Riemannian submersions from real and complex pseudo-hyperbolic spaces. Diff. Geom. and appl. 16 1, 79-84 (2002).
  • [5] Caldarella, A.V.: On para-quaternionic submersions between para-quaternionic Kähler manifolds. Acta Applicandae Mathematicae. 112 1, 1-14 (2010).
  • [6] Chen, B. Y.: Classification of flat Lagrangian H-umbilical submanifolds in para-Kähler n-plane. International Electronic Journal of Geometry. 4 1, 1-14 (2011).
  • [7] Falcitelli, M., Ianus, S., Pastore, A. M.: Riemannian Submersions and Related Topics.World Scientific. (2004).
  • [8] Gilkey, P., Itoh, M., Park, J.H.: Anti-invariant Riemannian submersions: A Lietheoretical approach. Taiwanese J. Math. 20 4, 787-800, (2016).
  • [9] Gündüzalp, Y.: Slant submersions in paracontact geometry. Hacet. J. Math. Stat. 49 2 , 822-834 (2020).
  • [10] Gündüzalp, Y.: Almost para-Hermitian submersions. Matematicki Vesnik. 68 4, 241-253 (2016).
  • [11] Gündüzalp, Y.: Anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds. Journal of Function Spaces and Applications. 2013 (2013) .
  • [12] Gündüzalp, Y.: Anti-invariant Pseudo-Riemannian Submersions and Clairaut Submersions from Paracosymplectic Manifolds. Mediterr. J. Math. 16 4, 1-18 (2019).
  • [13] Gündüzalp, Y.: Neutral slant submersions in paracomplex geometry, Afr. Mat. 32 5, 1095-1110 (2021).
  • [14] Gündüzalp, Y., Akyol, M.A.:Conformal slant submersions from cosymplectic manifolds. Turk. J. Math. 42 5, 2672–2689 (2018).
  • [15] Gray, A.: Pseudo-Riemannian almost product manifolds and submersions. Journal of Mathematics and Mechanics. 16 7, 715-737 (1967).
  • [16] Ianus, S., Mazzocco, R., Vilcu, G. E.: Riemannian submersions from quaternionic manifolds. Acta Applicandae Mathematicae. 104 1, 83-89 (2008).
  • [17] Ianus, S., Vilcu, G.E., Voicu, R.C.: Harmonic maps and Riemannian submersions between manifolds endowed with special structures. Banach Center Publications.93 277-288, (2011).
  • [18] Ivanov, S., Zamkovoy, S.: Para-Hermitian and para-quaternionic manifolds. Differential Geometry and its Applications. 23 2, 205-234 (2005).
  • [19] Erken, I.K., Murathan, C.: On slant Riemannian submersions for cosymplectic manifolds. Bull. Korean Math. Soc. 51 6 (2014).
  • [20] Lee, J. W., Şahin, B.: Pointwise slant submersions. Bull. Korean Math. Soc. 51 4, 1115–1126 (2014).
  • [21] Lee, C.W., Lee, J.W., Şahin B., Vîlcu, G.E.: Optimal inequalities for Riemannian maps and Riemannian submersions involving Casorati curvatures. Annali di Matematica Pura ed Applicata.200 3 1277-1295 (2021).
  • [22] O‘Neill, B.: The fundamental equations of a submersion. Michigan Mathematical Journal. 13 4, 459-469 (1966).
  • [23] Özdemir, F., Sayar, C., Tas.tan, H.M.: Semi-invariant submersions whose total manifolds are locally product Riemannian. Quaestiones Mathematicae. 40 7, 909-926 (2017).
  • [24] Prvanovic$\acute{c}$, M.: Holomorphically projective transformations in a locally product space. Math. Balkanica 1 , 195-213 (1971).
  • [25] Park, K.S.: H-slant submersions. Bull. Korean Math. Soc. 49 2, 329-338 (2012).
  • [26] Park, K.S., Prasad, R.: Semi-slant submersions. Bull. Korean Math. Soc. 50 3, 951-962 (2013).
  • [27] Prasad, R., Shukla, S. S., Kumar, S.: On Quasi-bi-slant Submersions. Mediterr. J. Math. 16 6, 1-18 (2019).
  • [28] Sepet, S. A., Ergut, M.: Pointwise slant submersions from cosymplectic manifolds. Turkish J.Math.40 3, 582-593 (2016).
  • [29] Sarı R., Akyol M.A.: Hemi-slant $\xi^\bot $ -Riemannian submersions in contact geometry. Filomat. 34 11, 3747–3758 (2020).
  • [30] Şahin, B.: Anti-invariant Riemannian submersions from almost Hermitian manifolds. Central European J.Math. 8 3, 437-447 (2010).
  • [31] Şahin, B.: Slant submersions from almost Hermitian manifolds. Bull. Math. Soc.Sci. Math. Roumanie Tome. 54 102, 93-105 (2011).
  • [32] Şahin, B.: Riemannian submersions from almost Hermitian manifolds. Taiwanese J. Math. 17 2, 629-659 (2013).
  • [33] Şahin, B.: Semi-invariant Submersions from Almost Hermitian Manifold. Canadian Mathematical Bulletin. 56 1, 173-183 (2013).
  • [34] Şahin, B.: Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications. Academic Press, (2017).
  • [35] Tastan, H. M., Şahin B., Yanan, ¸S.: Hemi-slant submersions. Mediterr. J. Math. 13 4, 2171–2184 (2016).
  • [36] Vîlcu, G.E.:Almost product structures on statistical manifolds and para-Kähler-like statistical submersions. Bulletin des Sciences Mathématiques. 171, 103018 (2021).
  • [37] Watson, B.: Almost Hermitian submersions. Journal of Differential Geometry. 11 1, 147-165 (1976).

Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry

Year 2022, Volume: 15 Issue: 2, 253 - 265, 31.10.2022
https://doi.org/10.36890/iejg.1033345

Abstract

In this paper, we examine the proper semi-slant pseudo-Riemannian submersions in para-Kaehler geometry and prove some fundamental results on such submersions. In particular we obtain curvature relations in para-Kaehler space forms. Moreover, we provide examples of proper semi-slant pseudo-Riemannian submersions.

References

  • [1] Akyol, M.A., Sarı, R.: On semi-slant $\xi^\bot $ -Riemannian submersions, Preprint arxiv:1704.01412 (2017).
  • [2] Alegre, P., Carriazo, A.: Slant submanifolds of para-Hermitian manifolds. Mediterr. J. Math. 14 (5), 1-14 (2017).
  • [3] Alegre, P., Carriazo, A.: Bi-slant submanifolds of para-Hermitian manifolds. Mathematics. 7 (7), 618 (2019).
  • [4] Baditoiu, G., Ianus, S.: Semi-Riemannian submersions from real and complex pseudo-hyperbolic spaces. Diff. Geom. and appl. 16 1, 79-84 (2002).
  • [5] Caldarella, A.V.: On para-quaternionic submersions between para-quaternionic Kähler manifolds. Acta Applicandae Mathematicae. 112 1, 1-14 (2010).
  • [6] Chen, B. Y.: Classification of flat Lagrangian H-umbilical submanifolds in para-Kähler n-plane. International Electronic Journal of Geometry. 4 1, 1-14 (2011).
  • [7] Falcitelli, M., Ianus, S., Pastore, A. M.: Riemannian Submersions and Related Topics.World Scientific. (2004).
  • [8] Gilkey, P., Itoh, M., Park, J.H.: Anti-invariant Riemannian submersions: A Lietheoretical approach. Taiwanese J. Math. 20 4, 787-800, (2016).
  • [9] Gündüzalp, Y.: Slant submersions in paracontact geometry. Hacet. J. Math. Stat. 49 2 , 822-834 (2020).
  • [10] Gündüzalp, Y.: Almost para-Hermitian submersions. Matematicki Vesnik. 68 4, 241-253 (2016).
  • [11] Gündüzalp, Y.: Anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds. Journal of Function Spaces and Applications. 2013 (2013) .
  • [12] Gündüzalp, Y.: Anti-invariant Pseudo-Riemannian Submersions and Clairaut Submersions from Paracosymplectic Manifolds. Mediterr. J. Math. 16 4, 1-18 (2019).
  • [13] Gündüzalp, Y.: Neutral slant submersions in paracomplex geometry, Afr. Mat. 32 5, 1095-1110 (2021).
  • [14] Gündüzalp, Y., Akyol, M.A.:Conformal slant submersions from cosymplectic manifolds. Turk. J. Math. 42 5, 2672–2689 (2018).
  • [15] Gray, A.: Pseudo-Riemannian almost product manifolds and submersions. Journal of Mathematics and Mechanics. 16 7, 715-737 (1967).
  • [16] Ianus, S., Mazzocco, R., Vilcu, G. E.: Riemannian submersions from quaternionic manifolds. Acta Applicandae Mathematicae. 104 1, 83-89 (2008).
  • [17] Ianus, S., Vilcu, G.E., Voicu, R.C.: Harmonic maps and Riemannian submersions between manifolds endowed with special structures. Banach Center Publications.93 277-288, (2011).
  • [18] Ivanov, S., Zamkovoy, S.: Para-Hermitian and para-quaternionic manifolds. Differential Geometry and its Applications. 23 2, 205-234 (2005).
  • [19] Erken, I.K., Murathan, C.: On slant Riemannian submersions for cosymplectic manifolds. Bull. Korean Math. Soc. 51 6 (2014).
  • [20] Lee, J. W., Şahin, B.: Pointwise slant submersions. Bull. Korean Math. Soc. 51 4, 1115–1126 (2014).
  • [21] Lee, C.W., Lee, J.W., Şahin B., Vîlcu, G.E.: Optimal inequalities for Riemannian maps and Riemannian submersions involving Casorati curvatures. Annali di Matematica Pura ed Applicata.200 3 1277-1295 (2021).
  • [22] O‘Neill, B.: The fundamental equations of a submersion. Michigan Mathematical Journal. 13 4, 459-469 (1966).
  • [23] Özdemir, F., Sayar, C., Tas.tan, H.M.: Semi-invariant submersions whose total manifolds are locally product Riemannian. Quaestiones Mathematicae. 40 7, 909-926 (2017).
  • [24] Prvanovic$\acute{c}$, M.: Holomorphically projective transformations in a locally product space. Math. Balkanica 1 , 195-213 (1971).
  • [25] Park, K.S.: H-slant submersions. Bull. Korean Math. Soc. 49 2, 329-338 (2012).
  • [26] Park, K.S., Prasad, R.: Semi-slant submersions. Bull. Korean Math. Soc. 50 3, 951-962 (2013).
  • [27] Prasad, R., Shukla, S. S., Kumar, S.: On Quasi-bi-slant Submersions. Mediterr. J. Math. 16 6, 1-18 (2019).
  • [28] Sepet, S. A., Ergut, M.: Pointwise slant submersions from cosymplectic manifolds. Turkish J.Math.40 3, 582-593 (2016).
  • [29] Sarı R., Akyol M.A.: Hemi-slant $\xi^\bot $ -Riemannian submersions in contact geometry. Filomat. 34 11, 3747–3758 (2020).
  • [30] Şahin, B.: Anti-invariant Riemannian submersions from almost Hermitian manifolds. Central European J.Math. 8 3, 437-447 (2010).
  • [31] Şahin, B.: Slant submersions from almost Hermitian manifolds. Bull. Math. Soc.Sci. Math. Roumanie Tome. 54 102, 93-105 (2011).
  • [32] Şahin, B.: Riemannian submersions from almost Hermitian manifolds. Taiwanese J. Math. 17 2, 629-659 (2013).
  • [33] Şahin, B.: Semi-invariant Submersions from Almost Hermitian Manifold. Canadian Mathematical Bulletin. 56 1, 173-183 (2013).
  • [34] Şahin, B.: Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications. Academic Press, (2017).
  • [35] Tastan, H. M., Şahin B., Yanan, ¸S.: Hemi-slant submersions. Mediterr. J. Math. 13 4, 2171–2184 (2016).
  • [36] Vîlcu, G.E.:Almost product structures on statistical manifolds and para-Kähler-like statistical submersions. Bulletin des Sciences Mathématiques. 171, 103018 (2021).
  • [37] Watson, B.: Almost Hermitian submersions. Journal of Differential Geometry. 11 1, 147-165 (1976).
There are 37 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Esra Başarır Noyan 0000-0001-6535-7498

Yılmaz Gündüzalp 0000-0002-0932-949X

Early Pub Date July 23, 2022
Publication Date October 31, 2022
Acceptance Date October 12, 2022
Published in Issue Year 2022 Volume: 15 Issue: 2

Cite

APA Başarır Noyan, E., & Gündüzalp, Y. (2022). Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry. International Electronic Journal of Geometry, 15(2), 253-265. https://doi.org/10.36890/iejg.1033345
AMA Başarır Noyan E, Gündüzalp Y. Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry. Int. Electron. J. Geom. October 2022;15(2):253-265. doi:10.36890/iejg.1033345
Chicago Başarır Noyan, Esra, and Yılmaz Gündüzalp. “Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry”. International Electronic Journal of Geometry 15, no. 2 (October 2022): 253-65. https://doi.org/10.36890/iejg.1033345.
EndNote Başarır Noyan E, Gündüzalp Y (October 1, 2022) Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry. International Electronic Journal of Geometry 15 2 253–265.
IEEE E. Başarır Noyan and Y. Gündüzalp, “Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry”, Int. Electron. J. Geom., vol. 15, no. 2, pp. 253–265, 2022, doi: 10.36890/iejg.1033345.
ISNAD Başarır Noyan, Esra - Gündüzalp, Yılmaz. “Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry”. International Electronic Journal of Geometry 15/2 (October 2022), 253-265. https://doi.org/10.36890/iejg.1033345.
JAMA Başarır Noyan E, Gündüzalp Y. Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry. Int. Electron. J. Geom. 2022;15:253–265.
MLA Başarır Noyan, Esra and Yılmaz Gündüzalp. “Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry”. International Electronic Journal of Geometry, vol. 15, no. 2, 2022, pp. 253-65, doi:10.36890/iejg.1033345.
Vancouver Başarır Noyan E, Gündüzalp Y. Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry. Int. Electron. J. Geom. 2022;15(2):253-65.