## Dhriti Patra - Certain Paracontact Metrics Satisfying the Critical Point Equation

cm:10549 - Communications in Mathematics, February 14, 2023, Volume 32 (2024), Issue 1 - https://doi.org/10.46298/cm.10549
Certain Paracontact Metrics Satisfying the Critical Point Equation

Authors: Dhriti Patra

The aim of this paper is to study theCPE (Critical Point Equation) on some paracontact metric manifolds.First, we prove that if a para-Sasakian metric satisfies the CPE,then it is Einstein with constant scalar curvature -2n(2n+1). Next,we prove that if $(\kappa,\mu)$-paracontact metric satisfies theCPE, then it is locally isometric to the product of a flat$(n+1)$-dimensional manifold and $n$-dimensional manifold ofnegative constant curvature$-4$.

Volume: Volume 32 (2024), Issue 1
Published on: February 14, 2023
Accepted on: December 27, 2022
Submitted on: December 27, 2022
Keywords: The critical point equation,paracontact metric manifold,para-Sasakian manifold,(k,µ)-paracontact manifold,[MATH]Mathematics [math]