Journal ArticleDOI

# Ricci semisymmetric almost kenmotsu manifolds with nullity distributions

01 Jan 2018-Filomat (National Library of Serbia)-Vol. 32, Iss: 1, pp 179-186
Abstract: The object of the present paper is to characterize Ricci semisymmetric almost Kenmotsu manifolds with its characteristic vector field \xi belonging to the (k,\mu )^{`}-nullity distribution and (k,\mu )-nullity distribution respectively. Finally, an illustrative example is given.

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Abstract: In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant $\varphi$-sectional curvature, and prove the structure theorem for $\xi$-conformally flat and $\varphi$-conformally flat Kenmotsu pseudo-metric manifolds. Next, we consider Ricci solitons on this manifolds. In particular, we prove that an $\eta$-Einstein Kenmotsu pseudo-metric manifold of dimension higher than 3 admitting a Ricci soliton is Einstein, and a Kenmotsu pseudo-metric 3-manifold admitting a Ricci soliton is of constant curvature $-\varepsilon$.

8 citations

### Cites background from "Ricci semisymmetric almost kenmotsu..."

• ...Almost Kenmotsu manifolds are the generalization of Kenmotsu manifolds and are studied under various geometric conditions in [16, 17, 18, 25, 33, 34, 12, 15]....

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Journal ArticleDOI
Uday Chand De1, Dibakar Dey1Institutions (1)
09 Aug 2019-
Abstract: The object of the present paper is to characterize Ricci pseudosymmetric and Ricci semisymmetric almost Kenmotsu manifolds with (k; μ)-, (k; μ)′-, and generalized (k; μ)-nullity distributions. We also characterize (k; μ)-almost Kenmotsu manifolds satisfying the condition R ⋅ S = LꜱQ(g; S2).

6 citations

### Cites background from "Ricci semisymmetric almost kenmotsu..."

• ...[5] studied Ricci semisymmetric almost Kenmotsu manifolds with nullity distributions....

[...]

Journal ArticleDOI
Dibakar Dey1Institutions (1)
Abstract: In the present paper, we characterize Ricci symmetric almost Kenmotsu manifolds under several constraints and proved that they are Einstein manifolds As a consequence, we obtain several corollaries Finally, an illustrative example is presented to verify our results

##### References
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Book
08 Jan 2002-
Abstract: Preface * 1. Symplectic Manifolds * 2. Principal S1-bundles * 3. Contact Manifolds * 4. Associated Metrics * 5. Integral Submanifolds and Contact Transformations * 6. Sasakian and Cosymplectic Manifolds * 7. Curvature of Contact Metric Manifolds * 8. Submanifolds of Kahler and Sasakian Manifolds * 9. Tangent Bundles and Tangent Sphere Bundles * 10. Curvature Functionals and Spaces of Associated Metrics * 11. Negative Xi-sectional Curvature * 12. Complex Contact Manifolds * 13. Additional Topics in Complex Geometry * 14. 3-Sasakian Manifolds * Bibliography * Subject Index * Author Index

1,643 citations

Book
01 Jan 1976-
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.

1,173 citations

• ...On the other hand, an odd dimensional manifold M2n+1(n ≥ 1) is said to admit an almost contact structure, sometimes called a (φ, ξ, η)-structure, if it admits a tensor field φ of type (1, 1), a vector field ξ and a 1-form η satisfying [1, 2] φ2 = −I + η ⊗ ξ, η(ξ) = 1, φξ = 0, η ◦ φ = 0....

[...]

Journal ArticleDOI
Katsuei Kenmotsu1Institutions (1)
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

539 citations

• ...A Kenmotsu manifold [10] can be defined as a normal almost contact metric manifold such that dη = 0 and dΦ = 2η ∧ Φ where Φ = 1(X, φY)....

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Journal ArticleDOI

353 citations

### "Ricci semisymmetric almost kenmotsu..." refers background in this paper

• ...Semisymmetric manifolds were classified by Szabó, locally in [16]....

[...]

Journal ArticleDOI
Abstract: This paper presents a study of contact metric manifolds for which the characteristic vector field of the contact structure satisfies a nullity type condition, condition (*) below. There are a number of reasons for studying this condition and results concerning it given in the paper: There exist examples in all dimensions; the condition is invariant underD-homothetic deformations; in dimensions>5 the condition determines the curvature completely; and in dimension 3 a complete, classification is given, in particular these include the 3-dimensional unimodular Lie groups with a left invariant metric.

314 citations

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