On \(\mathcal{T} \)-hypersurface of a paraSasakian manifold. (English) Zbl 1488.53166

Srivastava, Sachin Kumar; Sood, Kanika; Kumar, Anuj

Facta Univ., Ser. Math. Inf. 35, No. 4, 1003-1016 (2020).

Summary: The main purpose of this paper is to study transversal hypersurface (briefly, \( \mathcal{T} \)-hypersurface) \(P\) of a paraSasakian manifold \(M\). We derive results allied with totally geodesic and totally umbilical \(\mathcal{T} \)-hypersurface of \(M\). The necessary and sufficient condition for normality of \((\mathfrak{f},\mathfrak{g},\mu,\upsilon,\delta)\)-structure is established. Examples of \(\mathcal{T} \)-hypersurface are also illustrated.

MSC:

53C25	Special Riemannian manifolds (Einstein, Sasakian, etc.)
53D15	Almost contact and almost symplectic manifolds

Keywords:

para-Sasakian manifold; pseudo-metric; hypersurface; \((\mathfrak{f},\mathfrak{g},\mu,\upsilon,\delta)\)-structure; geodesic

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