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Journal ArticleDOI

Certain Curvature Conditions on Kenmotsu Manifolds and ★-η;-Ricci Solitons

30 Jan 2023-Axioms-Vol. 12, Iss: 2, pp 140-140
TL;DR: In this paper , the authors investigated the properties of a 3-dimensional Kenmotsu manifold satisfying certain curvature conditions endowed with Ricci solitons and showed that such a manifold is φ-Einstein.
Abstract: The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with 🟉-η-Ricci solitons. First we find some necessary conditions for such a manifold to be φ-Einstein. Then, we study the notion of 🟉-η-Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results.

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Citations
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Journal ArticleDOI
25 Apr 2023-Symmetry
TL;DR: In this paper , the authors derived the necessary conditions of a CR-warped product submanifolds in Ka-hler manifold to be an Einstein manifold in the impact of gradient Ricci soliton.
Abstract: In this article, we derived an equality for CR-warped product in a complex space form which forms the relationship between the gradient and Laplacian of the warping function and second fundamental form. We derived the necessary conditions of a CR-warped product submanifolds in Ka¨hler manifold to be an Einstein manifold in the impact of gradient Ricci soliton. Some classification of CR-warped product submanifolds in the Ka¨hler manifold by using the Euler–Lagrange equation, Dirichlet energy and Hamiltonian is given. We also derive some characterizations of Einstein warped product manifolds under the impact of Ricci Curvature and Divergence of Hessian tensor.

10 citations

References
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Book
01 Jan 1976
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.
Abstract: Contact manifolds.- Almost contact manifolds.- Geometric interpretation of the contact condition.- K-contact and sasakian structures.- Sasakian space forms.- Non-existence of flat contact metric structures.- The tangent sphere bundle.

1,259 citations

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701 citations

Journal ArticleDOI
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
Abstract: Recently S. Tanno has classified connected almostcontact Riemannian manifolds whose automorphism groups have themaximum dimension [9]. In his classification table the almost contactRiemannian manifolds are divided into three classes: (1) homogeneousnormal contact Riemannian manifolds with constant 0-holomorphic sec-tional curvature if the sectional curvature for 2-planes which contain

614 citations

Journal ArticleDOI
01 Jan 1940

273 citations

01 Jan 1970
TL;DR: In this paper, the Curvature tensor has been defined and its properties have been elaborated in terms of physical and geometric properties, including its properties and properties of curvature tensors.
Abstract: In this paper we have defined the Curvature tensor and elaborated its various physical and geometric properties.

110 citations