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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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Special symplectic six-manifolds
Diego Conti,Adriano Tomassini +1 more
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Classification of homogeneous almost cosymplectic three-manifolds ☆
TL;DR: In this article, the authors classify simply connected homogeneous almost cosymplectic 3-manifolds into Lie groups and Riemannian product of type R × N, where N is a Kahler surface of constant curvature.
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Einstein manifolds with skew torsion
TL;DR: In this paper, the first systematic investigation of manifolds that are Einstein for a connection ∇ with skew symmetric torsion is presented, and the longest part of the paper is devoted to the systematic construction of large families of examples.
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Sasakian Geometry, Homotopy Spheres and Positive Ricci Curvature
TL;DR: In this article, it was shown that the moduli space of Sasakian structures has infinitely many positive components determined by inequivalent underlying contact structures on odd-dimensional homotopy spheres.
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Riemannian submersions from almost contact metric manifolds
TL;DR: In this paper, the structure equation of a contact-complex Riemannian submersion was obtained and applied to almost cosymplectic manifolds with Kahler fibres.