Searcharxiv⌕ Search

arXiv subjects

Mukut Mani Tripathi

Publications and source records attributed to Mukut Mani Tripathi.

24 records · Page 2Linked to original sources
arXiv2009

Indefinite almost paracontact metric manifolds

In this paper we introduce the concept of $(\varepsilon)$-almost paracontact manifolds, and in particular, of $(\varepsilon)$-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of $(\varepsilon)$-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it can not admit an $(\varepsilon)$-para Sasakian structure. We show that, for an $(\varepsilon)$-para Sasakian manifold, the conditions of being symmetric, semi-symmetric or of constant sectional curvature are all identical. It is shown that a symmetric spacelike (resp. timelike) $(\varepsilon)$-para Sasakian manifold $M^{n}$ is locally isometric to a pseudohyperbolic space $H_ν^{n}(1)$ (resp. pseudosphere $S_ν^{n}(1)$). In last, it is proved that for an $(\varepsilon)$-para Sasakian manifold, the conditions of being Ricci-semisymmetric, Ricci-symmetric and Einstein are all identical.

math.DG↗
arXiv2008

C-totally real warped product submanifolds

We obtain a basic inequality involving the Laplacian of the warping function and the squared mean curvature of any warped product isometrically immersed in a Riemannian manifold without assuming any restriction on the Riemann curvature tensor of the ambient manifold. Applying this general theory, we obtain basic inequalities involving the Laplacian of the warping function and the squared mean curvature of $C$-totally real warped product submanifolds of $(κ,μ) $-space forms, Sasakian space forms and non-Sasakian $(κ,μ) $-manifolds. Then we obtain obstructions to the existence of minimal isometric immersions of $C$-totally real warped product submanifolds in $(κ,μ) $-space forms, non-Sasakian $(κ,μ) $-manifolds and Sasakian space forms. In the last, we obtain an example of a warped product $C$-totally real submanifold of a non-Sasakian $(κ,μ) $-manifold, which satisfies the equality case of the basic inequality.

math.DG↗
arXiv2008

A new connection in a Riemannian manifold

In a Riemannian manifold, the existence of a new connection is proved. In particular cases, this connection reduces to several symmetric, semi-symmetric and quarter-symmetric connections; even some of them are not introduced so far. We also find formula for curvature tensor of this new connection.

math.DG↗
arXiv2008

Ricci solitons in contact metric manifolds

In $N(k)$-contact metric manifolds and/or $(k,μ)$-manifolds, gradient Ricci solitons, compact Ricci solitons and Ricci solitons with $V$ pointwise collinear with the structure vector field $ξ$ are studied.

math.DG↗
arXiv2002

Ricci curvature of submanifolds in locally conformal almost cosymplectic manifolds

We obtain certain inequalities involving several intrinsic invariants namely scalar curvature, Ricci curvature and $k$-Ricci curvature, and main extrinsic invariant namely squared mean curvature for submanifolds in a locally conformal almost cosymplectic manifold with pointwise constant $% ϕ$-sectional curvature. Applying these inequalities we obtain several inequalities for slant, invariant, anti-invariant and {\em CR}-submanifolds. The equality cases are also discussed.

math-ph↗