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ISSN : 1226-0657

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Vol.28 No.2

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
Majhi, Pradip
Dey,, D. , & Majhi,, P. (2021). Sasakian 3-Manifolds Satisfying Some Curvature Conditions Associated to Ƶ-Tensor. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 28(2), 143-153, https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.2.143

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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