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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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Gauss and Ricci Equations in Contact Manifolds with a Quarter-Symmetric Metric Connection
Avik De,Siraj Uddin +1 more
TL;DR: In this paper, the extrinsic and intrinsic geometry of submanifolds of an almost contact metric manifold admitting a quarter-symmetric metric connection is studied, and the Gauss, Codazzi and Ricci equations corresponding to the connection are deduced.
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Curvature of $$C_5\oplus C_{12}$$ C 5 ⊕ C 12 -Manifolds
TL;DR: In this paper, the authors investigated the behavior of the curvature of C_5\oplus C_{12} -manifolds and gave some local classification theorems in dimension 2n+1/ge 5.
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New curvature tensors along Riemannian submersions
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Dirac Structures and Generalized Complex Structures on $TM \times \mathbf{R}^{h}$
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Variations of the total mixed scalar curvature of a distribution
TL;DR: In this paper, the authors examined the total mixed scalar curvature of a fixed distribution as a functional of a pseudo-Riemannian metric and developed variational formulas for quantities of extrinsic geometry of the distribution to find the critical points of this action.