Sasakian 3-Manifolds Satisfying Some Curvature Conditions Associated to Ƶ-Tensor

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2021, v.28 no.2, pp.143-153

https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.2.143

Dey, Dibakar (Department of Pure Mathematics, University of Calcutta)
Majhi, Pradip (Department of Pure Mathematics, University of Calcutta)

Dey, Dibakar, & Majhi, Pradip. (2021). SASAKIAN 3-MANIFOLDS SATISFYING SOME CURVATURE CONDITIONS ASSOCIATED TO Ƶ-TENSOR. 한국수학교육학회지시리즈B:순수및응용수학, 28(2), 143-153, https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.2.143

복사

Abstract

In this paper, we study some curvature properties of Sasakian 3-manifolds associated to Ƶ-tensor. It is proved that if a Sasakian 3-manifold (M, g) satisfies one of the conditions (1) the Ƶ-tensor is of Codazzi type, (2) M is Ƶ-semisymmetric, (3) M satisfies Q(Ƶ, R) = 0, (4) M is projectively Ƶ-semisymmetric, (5) M is Ƶ-recurrent, then (M, g) is of constant curvature 1. Several consequences are drawn from these results.

keywords: Sasakian 3-manifolds, Einstein manifolds, Codazzi type Z-tensor, Z-semisymmetry, projective Z-semisymmetry, Z-recurrent manifolds

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논문 상세

Vol.28 No.2

SASAKIAN 3-MANIFOLDS SATISFYING SOME CURVATURE CONDITIONS ASSOCIATED TO &#x01B5;-TENSOR

Sasakian 3-Manifolds Satisfying Some Curvature Conditions Associated to Ƶ-Tensor

Abstract

한국수학교육학회지시리즈B:순수및응용수학

SASAKIAN 3-MANIFOLDS SATISFYING SOME CURVATURE CONDITIONS ASSOCIATED TO Ƶ-TENSOR