E-Bochner curvature tensor on generalized Sasakian space forms

D.G. Prakasha; Vasant Chavan

doi:10.1016/j.crma.2015.10.027

Differential geometry

E-Bochner curvature tensor on generalized Sasakian space forms
[Tenseur de courbure de type E-Bochner sur les espaces formes sasakiens généralisés]

Présenté par : the Editorial Board

D.G. Prakasha ¹ ; Vasant Chavan ¹

¹ Department of Mathematics, Karnatak University, Dharwad, India

Comptes Rendus. Mathématique, Volume 354 (2016) no. 8, pp. 835-841.

Résumé
Abstract

Les espaces formes sasakiens généralisés sont devenus aujourd'hui un sujet assez spécialisé, mais de nombreux travaux contemporains s'attachent à l'étude de leurs propriétés et des tenseurs de courbure associés. Le but de cette note est d'étudier le tenseur de courbure de type E-Bochner sur les espaces formes sasakiens généralisés, et de caractériser les conditions pour qu'il soit respectivement : E-Bochner symétrique ( $\nabla B^{e} = 0$ ) ; E-Bochner semi-symétrique ( $R \cdot B^{e} = 0$ ) ; E-Bochner récurrent ; E-Bochner pseudo-symétrique ; tel que $B^{e} (ξ, X) \cdot S = 0$ ; tel que $B^{e} (ξ, X) \cdot R = 0$ .

Generalized Sasakian space forms have become today a rather specialized subject, but many contemporary works are concerned with the study of their properties and of their related curvature tensors. The goal of this paper is to study the E-Bochner curvature tensor on generalized Sasakian space forms, and to characterize the situations when it is, respectively: E-Bochner symmetric ( $\nabla B^{e} = 0$ ); E-Bochner semisymmetric ( $R \cdot B^{e} = 0$ ); E-Bochner recurrent; E-Bochner pseudosymmetric; such that $B^{e} (ξ, X) \cdot S = 0$ ; such that $B^{e} (ξ, X) \cdot R = 0$ .

Reçu le : 2014-11-03
Accepté le : 2015-10-12
Publié le : 2016-05-25

DOI : 10.1016/j.crma.2015.10.027

Affiliations des auteurs :

D.G. Prakasha ¹ ; Vasant Chavan ¹

¹ Department of Mathematics, Karnatak University, Dharwad, India

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     title = {E-Bochner curvature tensor on generalized {Sasakian} space forms},
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D.G. Prakasha; Vasant Chavan. E-Bochner curvature tensor on generalized Sasakian space forms. Comptes Rendus. Mathématique, Volume 354 (2016) no. 8, pp. 835-841. doi : 10.1016/j.crma.2015.10.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.10.027/

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