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On generalized Sasakian-space-forms with Weyl-conformal curvature tensor
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TLDR
In this paper, the authors studied Weyl-pseudosymmetric generalized Sasakianspace-forms and such space-forms satisfying the conditions C(ξ,X)R = 0 and C(X,S)S = 0, where R and S are the Riemannian curvature tensors and the Ricci tensor, respectively.Abstract:
The object of the this paper is to study Weyl-pseudosymmetric generalized Sasakianspace-forms and such space-forms satisfying the conditions C(ξ,X)R = 0 and C(ξ,X)S = 0, where C is the Weyl-conformal curvature tensor, R and S are the Riemannian curvature tensor and the Ricci tensor of the space-form respectively.read more
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Conformal Ricci soliton and quasi-Yamabe soliton on generalized Sasakian space form
TL;DR: In this article, a generalized Sasakian space form admits conformal Ricci soliton and quasi-Yamabe soliton, and it is shown that the potential function of a conformal gradient Ricci s soliton is constant.
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On the C-Bochner Curvature Tensor of Generalized Sasakian-Space-Forms
TL;DR: In this paper, the authors studied C-Bochner pseudosymmetric generalized Sasakian-space-forms and such space-forms with C-bochner curvature tensor satisfying the conditions
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E-Bochner curvature tensor on generalized Sasakian space forms
TL;DR: In this article, the E-Bochner curvature tensor on generalized Sasakian space forms is studied and the situations when it is symmetric, semisymmetric, recurrent, and pseudosymmetric are characterized.
Some results on Generalized Sasakian space forms
TL;DR: In this paper, the authors studied the curvature tensors in generalized Sasakian space forms and showed that the curvatures of the tensors are concircular, projective and projective.
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W-semisymmetric generalized Sasakian-space-forms
Abstract: Abstract We set a definition of a (0,2){(0,2)}-type tensor on the generalized Sasakian-space-forms. The necessary and sufficient conditions for W-semisymmetric generalized Sasakian-space forms are studied. Certain results of the Ricci solitons, the Killing vector fields and the closed 1-form on the generalized Sasakian-space-forms are derived. We also verify our results by taking non-trivial examples of the generalized Sasakian-space-forms.
References
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Book
Contact manifolds in Riemannian geometry
TL;DR: In this paper, the tangent sphere bundle is shown to be a contact manifold, and the contact condition is interpreted in terms of contact condition and k-contact and sasakian structures.
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Structure theorems on Riemannian spaces satisfying $R(X,\,Y)\cdot R=0$. I. The local version
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Generalized Sasakian-space-forms
TL;DR: In this paper, generalized Sasakian-space-forms are introduced and studied, by using some different geometric techniques such as Riemannian submersions, warped products or conformal and related transformations.
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On hypersurfaces satisfying a certain condition on the curvature tensor
TL;DR: In this article, the authors conjecture that the answer is affirmative in the case where M is irreducible and complete and d i m M ^ 3, where m is a complete hypersurface in a Euclidean space.