Year 2023,
Volume: 6 Issue: 2, 86 - 97, 30.06.2023
Pramod Kumar Rawat
,
Sushil Kumar
References
- [1] B. O’Neill, The fundamental equations of a submersion, Mich. Math. J., 33(13) (1966), 459-469.
- [2] A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16 (1967), 715-738.
- [3] B. Watson, Almost Hermitian submersions, Journal of differential geometry, 11(1) (1976), 147-165.
- [4] D. Chinea, Almost contact metric submersions, Rendiconti del Circolo Matematico del Palermo, 34(1) (1985) , 89-104.
- [5] D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics. 203, Birkhauser Boston, Basel, Berlin. (2002).
- [6] M. Falcitelli, A. M. Pastore, S. Ianus, Riemannian submersions and related topics, (2004).
- [7] B. Sahin, Riemannian submersions, Riemannian maps in Hermitian geometry, and their applications, Elsevier, Academic Press (2017).
- [8] B. Sahin, Slant submersions from Almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roum., 54(1) (2011), 93-105.
- [9] B. Sahin, Semi-invariant submersions from almost Hermitian manifolds, Canad. Math. Bull., 56(1) (2013), 173-183.
- [10] M. A. Akyol, R. Sari, E. Aksoy, Semi-invariant x? Riemannian submersions from Almost Contact metric manifolds, Int. J. Geom. Methods Mod. Phys. 14, (2017) no. 5, 1750075.
- [11] G. Ayar, Pseudo-protective and quasi-conformal curvature tensors on Riemannian submersions, Math. Methods Appl. Sci., 44, (2021) no. 17, 13791-13798.
- [12] P. Baird, J. C. Wood, Harmonic Morphism between Riemannian Manifolds, Oxford Science Publications, Oxford (2003).
- [13] S. Ianus, A. M. Ionescu, R. Mocanu, G.E. Vilcu, Riemannian submersions from Almost contact metric manifolds, Abh. Math. Semin. Univ. Humbg., 81(1) (2011), 101-114.
- [14] S. Ianus, R. Mazzocco, G. E. Vilcu, Riemannian submersion from quaternionic manifolds, Acta Appl. Math., 104(1) (2008), 83-89.
- [15] S. Kumar, R. Prasad, K. Kumar, On quasi bi-slant x?-Riemannian submersions, Differ. Geom.-Dyn. Syst., 24 (2022) 119-38.
- [16] S. Kumar, R. Prasad, S. K. Verma, Hemi-slant Riemannian submersions from cosymplectic manifolds, Tbil. Math. J., 15(4) (2022), 11-27.
- [17] S. Kumar, S. Kumar, S. Pandey, R. Prasad, Conformal hemi-slant submersions from almost Hermitian manifolds, Commun. Korean Math. Soc., 35 (2020) no. 3, 999-1018.
- [18] S. Kumar, S. Kumar, R. Prasad, A note on Csi-x?-Riemannian submersions from Kenmotsu manifolds, Bull. Transilv. Univ. Bras., 64(2) (2022), 151-166.
- [19] C. Murathana, I. K. Erkena, Anti-Invariant Riemannian Submersions from Cosymplectic Manifolds onto Riemannian Manifolds, Filomat, 29(7) (2015), 1429-1444.
- [20] R. Prasad, S. Kumar, Conformal anti-invariant submersions from nearly K¨ahler Manifolds, PJM., 8(2) (2019), 234-247.
- [21] R. Prasad, P. K. Singh, S. Kumar, On quasi bi-slant submersions from Sasakian manifolds onto Riemannian manifolds, Afr. Mat., 32(3) (2021), 403-417.
- [22] R. Prasad, M. A. Akyol, P. K. Singh, S. Kumar, On Quasi bi-slant submersions from Kenmotsu manifolds onto any Riemannian manifolds, J. Math. Ext., 16(6) (2022), (7)1-25.
- [23] R. Prasad, P. K. Singh, S. Kumar, Conformal semi-slant submersions from Lorentzian para Kenmotsu manifolds, Tbil. Math. J., 14(1) (2021), 191-209.
- [24] R. Prasad, M. A. Akyol, S. Kumar, P. K. Singh, Quasi bi-slant submersions in contact geometry, Cubo (Temuco)., 24(1) (2022), 1-20.
- [25] K. S. Park, R. Prasad, Semi-slant submersions, Bull. Korean Math. Soc, 50(3) (2013), 951-962.
- [26] B. Sahin, Riemannian submersion from almost Hermitian manifolds, Taiwanese J. Math., 17(2) (2013), 629-659.
- [27] B. Sahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Open Math., 8(3) (2010), 437-447.
- [28] M. A. Magid, Submersions from anti-de Sitter space with totally geodesic fibers, J. Differ. Geom., 16(2) (1981), 323-331.
- [29] M. Falcitelli, S. Ianus, A. M. Pastore, Riemannian Submersions and Related Topics, World Scientific Publishing Company (2004).
- [30] K. Matsumoto, On Lorentzian paracontact manifolds, Bull. of Yamagata Univ. Nat. Sci., 12(2) (1989), 151-156.
- [31] I. Mihai, R. Rosca, On Lorentzian P-Sasakian Manifolds, Classical Analysis World Scientific, Singapore, (1992), 155-169.
- [32] Y. Gunduzalp, Slant submersions from Lorentzian almost para- contact manifold, Gulf J. Math., 3(1) (2015), 18-28.
- [33] Y. Gunduzalp, B. Sahin, Paracontact semi-Riemannian submersions, Turkish J. Math. 37(1) (2013), 114-128.
- [34] S. Kumar, R. Prasad, P. K. Singh, Conformal semi-slant submersions from Lorentzian para Sasakian manifolds onto Riemannian manifolds, Commun. Korean Math. Soc. 34(2) (2019), 637-655.
- [35] R. Prasad, S. S. Shukla, S. Kumar, On quasi bi-slant submersions, Mediterr. J. Math., 16(6) (2019), 1-18.
- [36] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math., 509, Springer-Verlag, New York, (1976).
- [37] S. Longwap, F. Massamba, NE. Homti, On quasi-hemi-slant Riemannian submersion, J. Math. Comput. Sci., 34(1) (2019), 1-14.
- [38] H. M. Tastan, B. Sahin, S. Yanan, Hemi-slant submersions, Mediterr. J. Math., 13(4) (2016), 2171-2184.
On Quasi Hemi-Slant Submersions
Year 2023,
Volume: 6 Issue: 2, 86 - 97, 30.06.2023
Pramod Kumar Rawat
,
Sushil Kumar
Abstract
The paper deals with the notion of quasi hemi-slant submersions from Lorentzian para Sasakian manifolds onto Riemannian manifolds. These submersions are generalization of hemi-slant submersions and semi-slant submersions. In this paper, we also study the geometry of leaves of distributions which are involved in the definition of the submersion. Further, we obtain the conditions for such distributions to be integrable and totally geodesic. Moreover, we also give the characterization theorems for proper quasi hemi-slant submersions and provide some examples of it.
References
- [1] B. O’Neill, The fundamental equations of a submersion, Mich. Math. J., 33(13) (1966), 459-469.
- [2] A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16 (1967), 715-738.
- [3] B. Watson, Almost Hermitian submersions, Journal of differential geometry, 11(1) (1976), 147-165.
- [4] D. Chinea, Almost contact metric submersions, Rendiconti del Circolo Matematico del Palermo, 34(1) (1985) , 89-104.
- [5] D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics. 203, Birkhauser Boston, Basel, Berlin. (2002).
- [6] M. Falcitelli, A. M. Pastore, S. Ianus, Riemannian submersions and related topics, (2004).
- [7] B. Sahin, Riemannian submersions, Riemannian maps in Hermitian geometry, and their applications, Elsevier, Academic Press (2017).
- [8] B. Sahin, Slant submersions from Almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roum., 54(1) (2011), 93-105.
- [9] B. Sahin, Semi-invariant submersions from almost Hermitian manifolds, Canad. Math. Bull., 56(1) (2013), 173-183.
- [10] M. A. Akyol, R. Sari, E. Aksoy, Semi-invariant x? Riemannian submersions from Almost Contact metric manifolds, Int. J. Geom. Methods Mod. Phys. 14, (2017) no. 5, 1750075.
- [11] G. Ayar, Pseudo-protective and quasi-conformal curvature tensors on Riemannian submersions, Math. Methods Appl. Sci., 44, (2021) no. 17, 13791-13798.
- [12] P. Baird, J. C. Wood, Harmonic Morphism between Riemannian Manifolds, Oxford Science Publications, Oxford (2003).
- [13] S. Ianus, A. M. Ionescu, R. Mocanu, G.E. Vilcu, Riemannian submersions from Almost contact metric manifolds, Abh. Math. Semin. Univ. Humbg., 81(1) (2011), 101-114.
- [14] S. Ianus, R. Mazzocco, G. E. Vilcu, Riemannian submersion from quaternionic manifolds, Acta Appl. Math., 104(1) (2008), 83-89.
- [15] S. Kumar, R. Prasad, K. Kumar, On quasi bi-slant x?-Riemannian submersions, Differ. Geom.-Dyn. Syst., 24 (2022) 119-38.
- [16] S. Kumar, R. Prasad, S. K. Verma, Hemi-slant Riemannian submersions from cosymplectic manifolds, Tbil. Math. J., 15(4) (2022), 11-27.
- [17] S. Kumar, S. Kumar, S. Pandey, R. Prasad, Conformal hemi-slant submersions from almost Hermitian manifolds, Commun. Korean Math. Soc., 35 (2020) no. 3, 999-1018.
- [18] S. Kumar, S. Kumar, R. Prasad, A note on Csi-x?-Riemannian submersions from Kenmotsu manifolds, Bull. Transilv. Univ. Bras., 64(2) (2022), 151-166.
- [19] C. Murathana, I. K. Erkena, Anti-Invariant Riemannian Submersions from Cosymplectic Manifolds onto Riemannian Manifolds, Filomat, 29(7) (2015), 1429-1444.
- [20] R. Prasad, S. Kumar, Conformal anti-invariant submersions from nearly K¨ahler Manifolds, PJM., 8(2) (2019), 234-247.
- [21] R. Prasad, P. K. Singh, S. Kumar, On quasi bi-slant submersions from Sasakian manifolds onto Riemannian manifolds, Afr. Mat., 32(3) (2021), 403-417.
- [22] R. Prasad, M. A. Akyol, P. K. Singh, S. Kumar, On Quasi bi-slant submersions from Kenmotsu manifolds onto any Riemannian manifolds, J. Math. Ext., 16(6) (2022), (7)1-25.
- [23] R. Prasad, P. K. Singh, S. Kumar, Conformal semi-slant submersions from Lorentzian para Kenmotsu manifolds, Tbil. Math. J., 14(1) (2021), 191-209.
- [24] R. Prasad, M. A. Akyol, S. Kumar, P. K. Singh, Quasi bi-slant submersions in contact geometry, Cubo (Temuco)., 24(1) (2022), 1-20.
- [25] K. S. Park, R. Prasad, Semi-slant submersions, Bull. Korean Math. Soc, 50(3) (2013), 951-962.
- [26] B. Sahin, Riemannian submersion from almost Hermitian manifolds, Taiwanese J. Math., 17(2) (2013), 629-659.
- [27] B. Sahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Open Math., 8(3) (2010), 437-447.
- [28] M. A. Magid, Submersions from anti-de Sitter space with totally geodesic fibers, J. Differ. Geom., 16(2) (1981), 323-331.
- [29] M. Falcitelli, S. Ianus, A. M. Pastore, Riemannian Submersions and Related Topics, World Scientific Publishing Company (2004).
- [30] K. Matsumoto, On Lorentzian paracontact manifolds, Bull. of Yamagata Univ. Nat. Sci., 12(2) (1989), 151-156.
- [31] I. Mihai, R. Rosca, On Lorentzian P-Sasakian Manifolds, Classical Analysis World Scientific, Singapore, (1992), 155-169.
- [32] Y. Gunduzalp, Slant submersions from Lorentzian almost para- contact manifold, Gulf J. Math., 3(1) (2015), 18-28.
- [33] Y. Gunduzalp, B. Sahin, Paracontact semi-Riemannian submersions, Turkish J. Math. 37(1) (2013), 114-128.
- [34] S. Kumar, R. Prasad, P. K. Singh, Conformal semi-slant submersions from Lorentzian para Sasakian manifolds onto Riemannian manifolds, Commun. Korean Math. Soc. 34(2) (2019), 637-655.
- [35] R. Prasad, S. S. Shukla, S. Kumar, On quasi bi-slant submersions, Mediterr. J. Math., 16(6) (2019), 1-18.
- [36] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math., 509, Springer-Verlag, New York, (1976).
- [37] S. Longwap, F. Massamba, NE. Homti, On quasi-hemi-slant Riemannian submersion, J. Math. Comput. Sci., 34(1) (2019), 1-14.
- [38] H. M. Tastan, B. Sahin, S. Yanan, Hemi-slant submersions, Mediterr. J. Math., 13(4) (2016), 2171-2184.