On kenmotsu manifolds
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In this paper, the authors studied the Ricci tensor invariance of the Riemannian curvature tensor of the Kenmotsu manifold, which is derived from the almost contact Ricci manifold with some special conditions.Abstract:
The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semisymmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.read more
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From the Eisenhart problem to Ricci solitons in $f$-Kenmotsu manifolds
TL;DR: In this paper, the Eisenhart problem of finding parallel tensors for the symmetric case in the regular f-Kenmotsu framework is solved for the Ricci tensors.
On ( )-Trans-Sasakian Manifolds
S. S. Shukla,D. D. Singh +1 more
TL;DR: In this article, the authors introduce (� )-trans-Sasakian manifolds and give an example of such manifolds, and give some basic results regarding these manifolds.
Journal Article
On f-Recurrent Kenmotsu Manifolds
TL;DR: In this article, it was proved that a locally φ -recurrent K-meansu manifold is the Robertson-Walker spacetime, and a concrete example of a three-dimensional K-Mean manifold is given.
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ON A SEMI-SYMMETRIC METRIC CONNECTION IN AN (ε)-KENMOTSU MANIFOLD
TL;DR: In this paper, the authors studied a semi-symmetric metric connection in an (e)-Kenmotsu manifold whose projective curvature tensor satisfies certain curvature conditions.
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On invariant submanifolds of Kenmotsu manifolds
Uday Chand De,Pradip Majhi +1 more
TL;DR: In this paper, the authors obtained a necessary condition for a three dimensional invariant submanifold of a Kenmotsu manifold to be totally geodesic, where S, R are the Ricci tensor and curvature tensor respectively and α is the second fundamental form.
References
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Book
Semi-Riemannian Geometry With Applications to Relativity
TL;DR: In this article, the authors introduce Semi-Riemannian and Lorenz geometries for manifold theory, including Lie groups and Covering Manifolds, as well as the Calculus of Variations.
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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A class of almost contact riemannian manifolds
TL;DR: In this article, Tanno has classified connected almost contact Riemannian manifolds whose automorphism groups have themaximum dimension into three classes: (1) homogeneous normal contact manifolds with constant 0-holomorphic sec-tional curvature if the sectional curvature for 2-planes which contain
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