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Riemannian Geometry of Contact and Symplectic Manifolds
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TLDR
In this article, the authors describe a complex geometry model of Symplectic Manifolds with principal S1-bundles and Tangent Sphere Bundles, as well as a negative Xi-sectional Curvature.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 Indexread more
Citations
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The Fischer–Marsden conjecture and contact geometry
TL;DR: The Fischer–Marsden conjecture is considered within the frame-work of K-contact manifolds and if a non-Sasakian $$(\kappa ,\mu )$$(κ,μ)-contact metric satisfies $$\mathcal {L}^{*}_g(\lambda )=0$$Lg∗(λ)=0, then the metric is proved to be Einstein and is isometric to a unit sphere.
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On 3-dimensional normal almost contact metric manifolds satisfying certain curvature conditions
TL;DR: In this paper, the authors studied 3D normal almost contact metric manifolds satisfying certain curvature con- ditions and proved the existence of such a manifold by a concrete example.
Journal ArticleDOI
Almost Kenmotsu metric as a conformal Ricci soliton
Dibakar Dey,Pradip Majhi +1 more
TL;DR: It is shown that a -almost Kenmotsu manifolds admitting the conformal Ricci soliton is shown to be feasible and generalized.
Journal ArticleDOI
Geometry of contact strongly pseudo-convex cr-manifolds
TL;DR: In this paper, a contact strongly pseudo-convex CR-space form (of con- stant pseudo-holomorphic sectional curvature) was defined by using the Tana- ka-Webster connection.
Journal ArticleDOI
On a type of almost Kenmotsu manifolds with harmonic curvature tensors
Yaning Wang,Ximin Liu +1 more
TL;DR: In this article, the curvature tensor of a Ricci-flat almost Kahler manifold is shown to be harmonic if and only if it is locally isometric to a product space.