On generic submanifolds of LP-Sasakian manifolds with concurrent vector fields
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The object of the present paper is to deduce some important results on generic submanifolds and also generic product of LP-Sasakian manifolds with concurrent vector fields. Also, we provide a necessary and sufficient condition for which the invariant distribution $D$ and anti-invariant distribution $D^\perp$ of $M$ are Einstein. Also, we deduce an interesting necessary and sufficient condition for submanifolds of LP-Sasakian manifolds to be totally umbilical submanifolds. Especially we deal with the generic submanifolds admitting a Ricci soliton in LP-Sasakian manifolds endowed with concurrent vector fields.
Abstract
The object of the present paper is to deduce some important results on generic submanifolds and also generic product of LP-Sasakian manifolds with concurrent vector fields. Also, we provide a necessary and sufficient condition for which the invariant distribution $D$ and anti-invariant distribution $D^\perp$ of $M$ are Einstein. Also, we deduce an interesting necessary and sufficient condition for submanifolds of LP-Sasakian manifolds to be totally umbilical submanifolds. Especially we deal with the generic submanifolds admitting a Ricci soliton in LP-Sasakian manifolds endowed with concurrent vector fields.
참고문헌 (26)
- P. Alegre, "Semi-invariant submanifolds of Lorentzian Sasakian manifolds,", Demonstratio Math, 44(2), pp.391~406 (2011)
- C. S. Bagewadi, "Ricci solitons in Lorentzian α-Sasakian manifolds", Acta Math. Acad. Paedagog. Nyh´azi, 2(1), pp.59~68 (2012)
- Aurel Bejancu, "CR Submanifolds of a Kaehler Manifold. I", Proceedings of the American Mathematical Society, 69(1), pp.135~142 (1978), JSTOR[DOI]
- A. Bejancu, "Semi-invariant submanifolds of a Sasakian manifold", An. S¸tiint¸. Univ. “Al. I. Cuza” Ia¸si Sect¸. I a Mat, 27(1), pp.163~170 (1981)
- B.-Y. Chen, "Geometry of Submanifolds" (1973), Marcel Dekker, Inc
- Bang-Yen Chen, "SOME RESULTS ON CONCIRCULAR VECTOR FIELDS AND THEIR APPLICATIONS TO RICCI SOLITONS", 대한수학회보, 52(5), pp.1535~1547 (2015), 대한수학회
- B.-Y. Chen, "Ricci solitons and concurrent vector fields", Balkan J. Geom. Appl, 20(1), pp.14~25 (2015)
- Bang-Yen Chen, "Riemannian submanifolds with concircular canonical field", 대한수학회보, 56(6), pp.1525~1537 (2019), 대한수학회[DOI]
- T. Friedrich, "Almost contact manifolds, connections with torsion, and parallel spinors", J. Reine Angew. Math, 559, pp.217~236 (2003)[DOI]
- Amalendu Ghosh, "Certain Contact Metrics as Ricci Almost Solitons", Results in Mathematics, 65(1-2), pp.81~94 (2014), Springer Science and Business Media LLC[DOI]
- R. S. Hamilton, "Three-manifolds with positive Ricci curvature", J. Differential Geometry, 17(2), pp.255~306 (1982)
- M. Kobayashi, "Semi-invariant submanifolds of a certain class of almost contact manifolds", Tensor, 43(1), pp.28~36 (1986)
- D. L. K. Kumar, "Concircular curvature tensor of Kenmotsu manifolds admitting generalized Tanaka-webster connection", J. Math. Comput. Sci, 94, pp.447~462 (2019)
- P. Majhi, "Concircular vectors field in (k, µ)-contact metric manifolds", Int. Electron. J. Geom, 11(1), pp.52~56 (2018)[DOI]
- K. Matsumoto, "On Lorentzian paracontact manifolds", Bull. Yamagata Univ. Natur. Sci, 12(2), pp.151~156 (1989)
- K. Matsumoto, "On a certain transformation in a Lorentzian para-Sasakian manifold", Tensor, 47(2), pp.189~197 (1988)
- Mohammed El Amine Mekki, "Generalised Ricci Solitons on Sasakian Manifolds", Kyungpook Mathematical Journal, 57(4), pp.677~682 (2017), 경북대학교 자연과학대학 수학과
- H. G. Nagaraja, "Ricci solitons in Kenmotsu manifolds", J. Inform. Math. Sci, 8, pp.29~36 (2016)
- B. O’Neill, "Semi-Riemannian Geometry" (1983), Academic Press, Inc
- A. Sarkar, "On invariant submanifolds of LP-Sasakian manifolds", Extracta Math, 27(1), pp.145~154 (2012)
- S. Sevin¸c, "Some results about concircular and concurrent vector fields on pseudo-Kaehler manifolds", J. Phys. Conferrence Series, 766, pp.1~6 (2016)
- R. Sharm, "Sasakian 3-manifold as a Ricci soliton represents the Heisenberg group", Int. J. Geom. Methods Mod. Phys, 8(1), pp.149~154 (2011)[DOI]
- K. Yan, "On the concurrent vector fields of immersed manifolds", Kodai Math. Sem. Rep, 23, pp.343~350 (1971)[DOI]
- K. Yano, "Generic submanifolds of Sasakian manifolds", Kodai Math. J, (2), pp.163~196 (1980)
- H. Yolda¸s, "On generic submanifold of Sasakian manifold with concurrent vector field", Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat, 68(2), pp.1983~1994 (2019)[DOI]
- Zhao Guojing, "Invariant sub-manifolds and modes of nonlinear autonomous systems", Applied Mathematics and Mechanics, 19(7), pp.687~693 (1998), Springer Science and Business Media LLC[DOI]