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Article Dans Une Revue (Article De Synthèse) Communications in Mathematics Année : 2023

Certain Paracontact Metrics Satisfying the Critical Point Equation

Dhriti Patra
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Résumé

The aim of this paper is to study the CPE (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 the CPE, then it is locally isometric to the product of a flat $(n+1)$-dimensional manifold and $n$-dimensional manifold of negative constant curvature $-4$.
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Dates et versions

hal-03904450 , version 1 (16-12-2022)
hal-03904450 , version 2 (02-02-2023)
hal-03904450 , version 3 (14-02-2023)

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Dhriti Patra. Certain Paracontact Metrics Satisfying the Critical Point Equation. Communications in Mathematics, 2023, Volume 32 (2024), Issue 1, ⟨10.46298/cm.10549⟩. ⟨hal-03904450v3⟩
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