Curvature properties of Quasi-Para-Sasakian Manifolds

TL;DR

This paper explores the curvature characteristics of quasi-Para-Sasakian manifolds, establishing fundamental properties and curvature identities, and classifying these manifolds based on their constant curvature values.

Contribution

It introduces new curvature identities for quasi-Para-Sasakian manifolds and characterizes their structure depending on the constant curvature, including conditions for paracosymplectic and para-Sasakian structures.

Findings

If the manifold has constant curvature K, then K ≤ 0.

For K=0, the manifold is paracosymplectic.

For K<0, the structure is a homothetic deformation of a para-Sasakian manifold.

Abstract

The present paper is devoted to quasi-Para-Sasakian manifolds. Basic properties of such manifolds are obtained and general curvature identities are investigated. Next it is proved that if $M$ is quasi-Para-Sasakian manifold of constant curvature $K$. Then $K$ $\leq 0$ and $(i)~$if $K=0$, the manifold is paracosymplectic, $(ii)$ if $K<0$, the quasi-para-Sasakian structure of $M$ is obtained by a homothetic deformation of a para-Sasakian structure.