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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
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Generalized (\kappa,\mu)-space forms
TL;DR: In this paper, generalized (kappa, ε)-space forms are introduced and studied for contact metric and trans-Sasakian space forms, and examples for all possible dimensions are presented.
Lightlike hypersurfaces of indefinite Sasakian manifolds with parallel symmetric bilinear forms
TL;DR: In this paper, the authors investigated light-like hypersurfaces of indefinite Sasakian manifold which are tangent to the structure vector field and proved that under some conditions, the geometry of such hypersurface M has a close relation with the geometrical properties of structure vector fields.
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The Critical Point Equation And Contact Geometry
TL;DR: In this paper, the authors considered the CPE conjecture in the frame-work of contact manifold and contact metric and proved that a complete contact metric satisfying the conjecture is Einstein and is isometric to a unit sphere.
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Volume of small balls and sub-Riemannian curvature in 3D contact manifolds
TL;DR: In this article, the volume of small sub-Riemannian balls in a contact 3-dimensional manifold has been shown to expand asymptotically with respect to geometric invariants.