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

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On The Ricci Symmetry of Almost Kenmotsu Manifolds

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

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Riemannian Geometry of Contact and Symplectic Manifolds

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

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A class of almost contact riemannian manifolds

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Sur une classe remarquable d'espaces de Riemann

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Almost contact structures and curvature tensors

We consider locally symmetric almost Kenmotsu manifolds showing that such a manifold is a Kenmotsu manifold if and only if the Lie derivative of the structure, with respect to the Reeb vector field $\xi$, vanishes. Furthermore, assuming that for a $(2n+1)$-dimensional locally symmetric almost Kenmotsu manifold such Lie derivative does not vanish and the curvature satisfies $R_{XY}\xi =0$ for any $X, Y$ orthogonal to $\xi$, we prove that the manifold is locally isometric to the Riemannian product of an $(n+1)$-dimensional manifold of constant curvature $-4$ and a flat $n$-dimensional manifold. We give an example of such a manifold.

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On The Ricci Symmetry of Almost Kenmotsu Manifolds

References

Riemannian Geometry of Contact and Symplectic Manifolds

A class of almost contact riemannian manifolds

Sur une classe remarquable d'espaces de Riemann

Almost contact structures and curvature tensors

Almost Kenmotsu manifolds and local symmetry

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Generalized kenmotsu manifolds