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Abstract
We first introduce quasi bi-slant Riemannian maps and study such Riemannian maps from Lorentzian para Sasakian manifolds into Riemannian manifolds. We give necessary and sufficient conditions for the integrability of the distributions which are involved in the definition of the quasi bi-slant Riemannian map and investigate their leaves. We also obtain totally geodesic conditions for such maps. Moreover, we provide some examples for this notion.
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References
- Baird, P. and Wood, J.C., Harmonic Morphisms Between Riemannian Manifolds, London Mathematical Society Monographs, Vol. 29 (Oxford University Press, The Clarendon Press, Oxford, 2003).
- Bilal, M., Kumar, S., Prasad, R., Haseeb, A., and Kumar S., On h-Quasi-Hemi-Slant Riemannian Maps, Axioms. 11(11) (2022) Page 641.
- Bourguignon, J.P. and Lawson, H.B., A mathematician’s visit to Kaluza-Klein theory, Rend. Semin. Mat. Univ. Politec. Torino Special Issue (1989), 143 − 163.
- Bourguignon, J.P. and Lawson, H.B., Stability and isolation phenomena for Yang-mills fields, Commun. Math. Phys. 79 (1981), 189 − 230.
- Falcitelli, M. Pastore, A.M. and Ianus, S., Riemannian submersions and related topics, World Scientific, River Edge, NJ, 2004.
- Fischer, A.E., Riemannian maps between Riemannian manifolds, Contemp. Math. 132 (1992), 331 − 366.
- Garcia-Rio, E. and Kupeli, D.N., Semi-Riemannian Maps and Their Applications, Kluwer Academic, Dordrecht, 1999.
- Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715 − 737.
- Gunduzalp, Y. and S¸ahin, B., Paracontact semi-Riemannian submersions, Turkish J. Math. 37(1) (2013), 114 − 128.
- Ianus, S. and Visinescu, M., Kaluza-Klein theory with scalar fields and generalized Hopf manifolds, Class. Quantum Gravit. 4 (1987), 1317 − 1325.
- Kumar, S., Prasad, R. and Singh, P.K., Conformal Semi-Slant Submersions from Lorentzian Para Sasakian Manifolds, Commun. Korean Math. Soc. 34(2)(2019), 637 − 655.
- Kumar, S., Bilal, M., Prasad, R., Haseeb, A., and Chen, Z., V-quasi-bi-slant Riemannian maps, Symmetry 14(7) (2022), page 1360.
- Magid, M.A., Submersions from anti-de Sitter space with totally geodesic fibers, J. Differential Geom. 16(2) (1981), 323 − 331.
- O’Neill, B., The fundamental equations of a submersion, Mich. Math. J. 13 (1966), 458−469.
- Park, K.S., Semi-slant Riemannian maps, Taiwanese Journal of Mathematics 17(3) (2013), 937 − 956.
- Prasad, R., Kumar, S., Kumar, S. and Vanli, A.T., On Quasi-Hemi-Slant Riemannian Maps, Gazi University Journal of Science 34(2) 2021, 477 − 491
- Prasad, R., and Kumar, S., Semi-slant Riemannian maps from almost contact metric manifolds into Riemannian manifolds, Tbilisi Math. J. 11(4) (2018), 19 − 34.
- Prasad, R., Mofarreh, F., Haseeb, A., and Verma, S.K., On quasi bi-slant Lorentzian submersions from LP-Sasakian manifolds, Journal Of Math. and Comp. Sci. 24(3) (2021), 186−200.
- S. ahin, B., Biharmonic Riemannian maps, Ann. Polon. Math. 102(1), (2011), 39 − 49.
- S. ahin, B., Hemi-slant Riemannian Maps, Mediterr. J. Math. (2017) DOI 10.1007/s00009-016-0817-21660-5446/17/010001-17.
- S. ahin, B., Invariant and anti-invariant Riemannian maps to Kahler manifolds, Int. J. Geom. Methods Mod. Phys. 7(3) (2010), 337 − 355.
- S. ahin, B., Riemannian submersions, Riemannian maps in Hermitian Geometry and their applications, Elsevier, Academic Press, 2017.
References
Baird, P. and Wood, J.C., Harmonic Morphisms Between Riemannian Manifolds, London Mathematical Society Monographs, Vol. 29 (Oxford University Press, The Clarendon Press, Oxford, 2003).
Bilal, M., Kumar, S., Prasad, R., Haseeb, A., and Kumar S., On h-Quasi-Hemi-Slant Riemannian Maps, Axioms. 11(11) (2022) Page 641.
Bourguignon, J.P. and Lawson, H.B., A mathematician’s visit to Kaluza-Klein theory, Rend. Semin. Mat. Univ. Politec. Torino Special Issue (1989), 143 − 163.
Bourguignon, J.P. and Lawson, H.B., Stability and isolation phenomena for Yang-mills fields, Commun. Math. Phys. 79 (1981), 189 − 230.
Falcitelli, M. Pastore, A.M. and Ianus, S., Riemannian submersions and related topics, World Scientific, River Edge, NJ, 2004.
Fischer, A.E., Riemannian maps between Riemannian manifolds, Contemp. Math. 132 (1992), 331 − 366.
Garcia-Rio, E. and Kupeli, D.N., Semi-Riemannian Maps and Their Applications, Kluwer Academic, Dordrecht, 1999.
Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715 − 737.
Gunduzalp, Y. and S¸ahin, B., Paracontact semi-Riemannian submersions, Turkish J. Math. 37(1) (2013), 114 − 128.
Ianus, S. and Visinescu, M., Kaluza-Klein theory with scalar fields and generalized Hopf manifolds, Class. Quantum Gravit. 4 (1987), 1317 − 1325.
Kumar, S., Prasad, R. and Singh, P.K., Conformal Semi-Slant Submersions from Lorentzian Para Sasakian Manifolds, Commun. Korean Math. Soc. 34(2)(2019), 637 − 655.
Kumar, S., Bilal, M., Prasad, R., Haseeb, A., and Chen, Z., V-quasi-bi-slant Riemannian maps, Symmetry 14(7) (2022), page 1360.
Magid, M.A., Submersions from anti-de Sitter space with totally geodesic fibers, J. Differential Geom. 16(2) (1981), 323 − 331.
O’Neill, B., The fundamental equations of a submersion, Mich. Math. J. 13 (1966), 458−469.
Park, K.S., Semi-slant Riemannian maps, Taiwanese Journal of Mathematics 17(3) (2013), 937 − 956.
Prasad, R., Kumar, S., Kumar, S. and Vanli, A.T., On Quasi-Hemi-Slant Riemannian Maps, Gazi University Journal of Science 34(2) 2021, 477 − 491
Prasad, R., and Kumar, S., Semi-slant Riemannian maps from almost contact metric manifolds into Riemannian manifolds, Tbilisi Math. J. 11(4) (2018), 19 − 34.
Prasad, R., Mofarreh, F., Haseeb, A., and Verma, S.K., On quasi bi-slant Lorentzian submersions from LP-Sasakian manifolds, Journal Of Math. and Comp. Sci. 24(3) (2021), 186−200.
S. ahin, B., Biharmonic Riemannian maps, Ann. Polon. Math. 102(1), (2011), 39 − 49.
S. ahin, B., Hemi-slant Riemannian Maps, Mediterr. J. Math. (2017) DOI 10.1007/s00009-016-0817-21660-5446/17/010001-17.
S. ahin, B., Invariant and anti-invariant Riemannian maps to Kahler manifolds, Int. J. Geom. Methods Mod. Phys. 7(3) (2010), 337 − 355.
S. ahin, B., Riemannian submersions, Riemannian maps in Hermitian Geometry and their applications, Elsevier, Academic Press, 2017.