On $\mathbf{\mathfrak{t}}$-hypersurfaces of Lorentzian para Kenmotsu manifolds

Rajendra Prasad; Pooja Gupta

doi:10.5269/bspm.64347

Prof. Rajendra Prasad University of Lucknow
Pooja Gupta University of Lucknow

Abstract

The main purpose of this paper is to study transversal hypersurface (briefly, $\mathfrak{T}$-hypersurface) of Lorentzian para Kenmotsu manifolds. It is proved that each $\mathfrak{T}$-hypersurface of Lorentzian almost paracontact manifold admits an almost product Lorentzian metric structure $(J,G)$. After that, we show that every $\mathfrak{T}$-hypersurface of Lorentzian almost paracontact manifold also admits a Lorentzian $(f,g,\mu,\nu, \lambda)$-structure and we derive some results allied with relationship between induced almost product Lorentzian metric structure $(J,G)$ and induced Lorentzian $(f,g,\mu,\nu, \lambda)$-structure. Example of $\mathfrak{T}$-hypersurface of Lorentzian para Kenmotsu manifold admitting Lorentzian $(f,g,\mu,\nu, \lambda)$-structure is also illustrated.

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References

Blair, D. E., Ludden, G. D., Hypersurfaces in almost contact manifolds, Tohuku Math. J. (2) 21 (1969), 354–362.

Eum, S. S., On complex hypersurfaces in normal almost contact spaces, Tensor (N.S.) 19 (1968), 45–50.

Goldberg, S. I., Yano, K., Noninvariant hypersurfaces of almost contact manifolds, J. Math. Soc. Japan 22 (1970), 25–34.

Ludden, G. D., Submanifolds of cosymplectic manifolds, J. Differential Geometry 4 (1970), 237–244.

O’Neill, B., Semi-Riemannian Geometry With Applications To Relativity, Academic Press, New York, 1983.

Lifschytz, G. and Ortiz, M., Quantum gravity effects at a black hole horizon, Nucl. Phys. B, 456(1995), 377-401.

Duggal, K. L. and Bejancu, A., Lightlike Submanifolds of semi-Riemannian Manifolds and Applications, Mathematics and its Applications, 364, Kluwer Academic Publishers, Dordrecht, 1996.

Yano, K and Okumara, M., On (f, g, u, v, λ)-structures, Kodai Math. Sem. Rep., 22(1970), 401-423.

Okumura, M., On some real hypersurfaces of a complex projective space, Trans. Am. Math. Soc., 212 (1975), 355-364.

Montiel, S., Real hypersurfaces of a complex hyperbolic space, J. Math. Soc., 37(3) (1985), 515-535.

Maeda, Y., On real hypersurfaces of a complex projective space, J. Math. Soc. Japan., 28 (3) (1976), 529-540.

Yano, K., Eum, S. S. and Ki, U-H., On transversal hypersurfaces of an almost contact manifold, Kodai Math. Sem. Rep., 24 (1972), 459-470.

Ahmad, M. and Shaikh, A. A., Transversal hypersurface of (LCS)n-manifold, Acta Math. Univ. Comenianae, 87(1) (2018), 107-116.

Prasad, R. and Tripathi, M. M., Transversal hypersurfaces of Kenmotsu manifold, Indian J. Pure Appl. Math., 34(3) (2003), 443-452.

Prasad, R. and Yadav, S. P., Transversal hypersurfaces with (f, g, u, v, λ)-structures of a nearly trans-Sasakian manifold, Advances in Pure. Appl. Math., 7(2) (2016), 115-121.

Adati, T., Hypersurfaces of almost paracontact Riemannian manifolds, TRU Math. 17 (1981),189–198.

Sato, I., On a structure similar to the almost contact structure, Tensor(N. S.), 30(1976), 219-224.

Matsumoto, K., On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Natur. Sci. 12(1989), 151–156.

Matsumoto, K., Mihai, I., On a certain transformation in a Lorentzian para-Sasakian manifold, Tensor (N.S.) 47 (1988), 189–197.

Matsumoto, K., Shaikh, A. A., and De, U. C., On Lorentzian para-Sasakian manifolds, Rend. Semin. Mat. Messina (II) (2000), suppl. 149–158.

Mihai, I., Rosca, R., On Lorentzian P-Sasakian manifolds, pp. 155–169 in: Classical Analysis, Proc. Kazimierz Dolny 1991, World Scientific, Singapore 1992.

Tripathi, M. M., De, U. C., Lorentzian almost paracontact manifolds and their submanifolds, J. Korea Soc. Math. Educ. 2 (2001), 101–125.

Tripathi, M. M., Shukla, S. S., On submanifolds of Lorentzian almost paracontact manifolds, Publ. Math. Debrecen 59 (2001), 327–338.

Haseeb, A., Prasad, R., Certain Results on Lorentzian Para-Kenmotsu Manifolds, Bol. Soc. Paran. Mat. 3 (2021), 201-220.

Prasad, R., Rai, A. K., Shukla, S.S., Tripathi, M.M., A Note on Transversal Hypersurfaces of Lorentzian Almost Paracontact Manifolds, Demonstratio Mathematica, 4 (2007).