Abstract
We investigate recurrent, Lie-recurrent, and Hopf lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a semi-symmetric metric connection. In these hypersurfaces, we obtain several new results. Moreover, we characterize that the total space (an indefinite generalized Sasakian space form) with a semi-symmetric metric connection is an indefinite Kenmotsu space form under various lightlike hypersurfaces.
Highlights
We investigate recurrent, Lie-recurrent, and Hopf lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a semi-symmetric metric connection
Riemannian manifold was introduced by Yano [2]. He proved that a Riemannian manifold admits a semi-symmetric metric connection whose curvature tensor vanishes if and only if a Riemannian manifold is conformally flat
In a semi-Riemannian manifold, Duggal and Sharma [3] studied some properties of the Ricci tensor, affine conformal motions, geodesics, and group manifolds admitting a semi-symmetric metric connection
Summary
An odd-dimensional pseudo-Riemannian manifold ( M, ḡ) is called an indefinite almost contact metric manifold if there exists an indefinite almost contact metric structure { J, ζ, θ, ḡ} with a (1, 1)-type tensor field J, a vector field ζ, and a 1-form θ such that. An indefinite almost contact metric manifold ( M, J, ζ, θ, ḡ) is called an indefinite trans-Sasakian e with respect to ḡ, there exist two smooth functions α and β manifold [9] if, for the Levi-Civita connection ∇ Such that e J )Ȳ = α{ ḡ( X, Ȳ )ζ − θ (Ȳ ) X } + β{ ḡ( J X, Ȳ )ζ − θ (Ȳ ) J X }.
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