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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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Mixed 3-Sasakian structures and curvature
TL;DR: In this paper, the authors studied the properties of the curvature of mixed 3-Sasakian structures, and proved that any manifold endowed with such a structure is Einstein.
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Examples of compact K-contact manifolds with no Sasakian metric
TL;DR: Using the Hard Lefschetz Theorem for Sasakian manifolds, this article found two examples of compact K-contact nilmanifolds with no compatible Sasakians in dimensions five and seven, respectively.
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Contact real hypersurfaces in the complex hyperbolic quadric
Sebastian Klein,Young Jin Suh +1 more
TL;DR: In this article, the geometry of contact real hypersurfaces with constant mean curvature in the complex hyperbolic quadric was discussed and the individual types (two types of tubes around totally geodesic submanifolds and one type of horosphere) that have been found in that classification were studied.
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K-contact metrics as Ricci solitons
Amalendu Ghosh,Ramesh Sharma +1 more
TL;DR: Ghosh et al. as mentioned in this paper studied Ricci solitons on a Riemannian manifold whose metric is a Ricci tensor and showed that Ricci is a generalization of the Einstein metric and is defined on the manifold by ( £ V g) + 2 S(X,Y) +2 R ij projected from the space of metrics onto its quotient modulodiffeomorphisms and scalings.
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Kähler contact distributions
TL;DR: In this paper, the generalized Tanaka connection on contact metric manifolds was introduced and a linear connection ∇ on the contact metric manifold was defined, which enables us to give a characterization in terms of ∇ of a strongly pseudo-convex C R -structure on M.