Screen Pseudo-Slant Lightlike Submersions from Indefinite Sasakian Manifolds onto Lightlike Manifolds
Yıl 2024,
Cilt: 17 Sayı: 2, 437 - 446, 27.10.2024
Shiv Sharma Shukla
,
Vipul Singh
Öz
As a generalization of screen slant lightlike submersions, we introduce the notion of screen pseudo-slant lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds. We give examples and prove a characterization theorem for the existence of such lightlike submersions. We also obtain integrability conditions of distributions involved in the definition of this class of lightlike submersions. Further, we find necessary and sufficient conditions for foliations determined by these distributions to be totally geodesic.
Kaynakça
- [1] Duggal, K. L., Bejancu, A.: Lightlike submanifolds of semi-Riemannian manifolds and applications. Mathematics and Its Applications.
Kluwer Publisher, Dordrecht (1996).
- [2] Duggal, K. L., Şahin, B.: Differential geometry of lightlike submanifolds. Frontiers in Mathematics. Birkhaüser Verlag, Basel (2010).
- [3] Duggal, K. L., Şahin, B.: Lightlike Submanifolds of indefinite Sasakian manifolds. Int. J. Math. Math. Sci., Article ID 57585 (2007)
- [4] Gray, A.: Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16(7), 715-737 (1967).
- [5] Gündüzalp, Y.: Neutral slant submersions in paracomplex geometry. Afr. Mat. 32(5-6), 1095-1110 (2021).
- [6] Gündüzalp, Y.: Slant submersions in paracontact geometry. Hacet. J. Math. Stat. 49(2), 822-834 (2020).
- [7] Kaushal, R., Kumar, R., Nagaich, R. K.: On the geometry of screen conformal submersions of semi-transversal lightlike submanifolds. Asian-Eur.
J. Math. 14(8), 1-13 (2021).
- [8] Noyan, E. Başarır, Gündüzalp, Y.: Proper semi-slant pseudo-Riemannian submersions in para-Kaehler geometry. Int. Electron. J. Geom. 15(2),
253-265 (2022).
- [9] Noyan, E. Başarır, Gündüzalp, Y.: Proper bi-slant pseudo-Riemannian submersions whose total manifolds are para-Kaehler manifolds Honam
Math. J. 44(3), 370-383 (2022).
- [10] O’Neill, B.: The fundamental equations of a submersion. Michigan Math. J. 13(4), 459-469 (1966).
- [11] O’Neill, B.: Semi-Riemannian geometry with applications to relativity. Academic Press. London (1983).
- [12] Prasad, R., Singh, P. K., Kumar, S.: Slant lightlike submersions from an indefinite nearly K¨ahler manifold into a lightlike manifold. J. Math. Comput.
Sci. 8(2), 225-240 (2018).
- [13] Sachdeva, R., Kumar, R., Bhatia, S. S.: Slant lightlike submersions from an indefinite almost Hermitian manifold into a lightlike manifold. Ukrainian
Math. J. 68(7), 1097-1107 (2016).
- [14] Şahin, B.: On a submersion between Reinhart lightlike manifolds and semi-Riemannian manifolds. Mediterr. J. Math. 5(3), 273-284 (2008).
- [15] Şahin, B., Gündüzalp, Y.: Submersions from semi-Riemannian manifolds onto lightlike manifolds. Hacet. J. Math. Stat. 39(1), 41-53 (2010).
- [16] Shukla, S. S., Yadav, A.: Screen pseudo-slant lightlike submanifolds of indefinite Sasakian manifolds. Mediterr. J. Math. 13, 789-802 (2016).
- [17] Shukla, S. S., Singh, V.: Screen slant lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds. Lobachevskii J. Math. 43(3),
697-708 (2022).
- [18] Shukla, S. S., Singh, V.: Transversal lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds. Commun. Korean Math.
Soc. 38(4), 1191-1213 (2023).
- [19] Shukla, S. S., Singh, V.: Radical transversal screen slant lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds. Int. J.
Geom. Methods Mod. Phys. 21(1), 1-21 (2024).
- [20] Shukla, S. S., Omar, S.: Screen pseudo-slant lightlike submersions. J. Indones. Math. 29(1), 64-74 (2023).
- [21] Takahashi, T.: Sasakian manifold with pseudo-Riemannian metric. Tohoku Math. J. 21(2), 271-290 (1969).
Yıl 2024,
Cilt: 17 Sayı: 2, 437 - 446, 27.10.2024
Shiv Sharma Shukla
,
Vipul Singh
Kaynakça
- [1] Duggal, K. L., Bejancu, A.: Lightlike submanifolds of semi-Riemannian manifolds and applications. Mathematics and Its Applications.
Kluwer Publisher, Dordrecht (1996).
- [2] Duggal, K. L., Şahin, B.: Differential geometry of lightlike submanifolds. Frontiers in Mathematics. Birkhaüser Verlag, Basel (2010).
- [3] Duggal, K. L., Şahin, B.: Lightlike Submanifolds of indefinite Sasakian manifolds. Int. J. Math. Math. Sci., Article ID 57585 (2007)
- [4] Gray, A.: Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16(7), 715-737 (1967).
- [5] Gündüzalp, Y.: Neutral slant submersions in paracomplex geometry. Afr. Mat. 32(5-6), 1095-1110 (2021).
- [6] Gündüzalp, Y.: Slant submersions in paracontact geometry. Hacet. J. Math. Stat. 49(2), 822-834 (2020).
- [7] Kaushal, R., Kumar, R., Nagaich, R. K.: On the geometry of screen conformal submersions of semi-transversal lightlike submanifolds. Asian-Eur.
J. Math. 14(8), 1-13 (2021).
- [8] Noyan, E. Başarır, Gündüzalp, Y.: Proper semi-slant pseudo-Riemannian submersions in para-Kaehler geometry. Int. Electron. J. Geom. 15(2),
253-265 (2022).
- [9] Noyan, E. Başarır, Gündüzalp, Y.: Proper bi-slant pseudo-Riemannian submersions whose total manifolds are para-Kaehler manifolds Honam
Math. J. 44(3), 370-383 (2022).
- [10] O’Neill, B.: The fundamental equations of a submersion. Michigan Math. J. 13(4), 459-469 (1966).
- [11] O’Neill, B.: Semi-Riemannian geometry with applications to relativity. Academic Press. London (1983).
- [12] Prasad, R., Singh, P. K., Kumar, S.: Slant lightlike submersions from an indefinite nearly K¨ahler manifold into a lightlike manifold. J. Math. Comput.
Sci. 8(2), 225-240 (2018).
- [13] Sachdeva, R., Kumar, R., Bhatia, S. S.: Slant lightlike submersions from an indefinite almost Hermitian manifold into a lightlike manifold. Ukrainian
Math. J. 68(7), 1097-1107 (2016).
- [14] Şahin, B.: On a submersion between Reinhart lightlike manifolds and semi-Riemannian manifolds. Mediterr. J. Math. 5(3), 273-284 (2008).
- [15] Şahin, B., Gündüzalp, Y.: Submersions from semi-Riemannian manifolds onto lightlike manifolds. Hacet. J. Math. Stat. 39(1), 41-53 (2010).
- [16] Shukla, S. S., Yadav, A.: Screen pseudo-slant lightlike submanifolds of indefinite Sasakian manifolds. Mediterr. J. Math. 13, 789-802 (2016).
- [17] Shukla, S. S., Singh, V.: Screen slant lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds. Lobachevskii J. Math. 43(3),
697-708 (2022).
- [18] Shukla, S. S., Singh, V.: Transversal lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds. Commun. Korean Math.
Soc. 38(4), 1191-1213 (2023).
- [19] Shukla, S. S., Singh, V.: Radical transversal screen slant lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds. Int. J.
Geom. Methods Mod. Phys. 21(1), 1-21 (2024).
- [20] Shukla, S. S., Omar, S.: Screen pseudo-slant lightlike submersions. J. Indones. Math. 29(1), 64-74 (2023).
- [21] Takahashi, T.: Sasakian manifold with pseudo-Riemannian metric. Tohoku Math. J. 21(2), 271-290 (1969).