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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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Book ChapterDOI
Curvature of Contact Metric Manifolds
TL;DR: The authors surveys a number of results and open questions concerning the curvature of Riemannian metrics associated to a contact form, including the curvatures of contact forms and contact boxes.
Journal ArticleDOI
Contact Semi-Riemannian Structures in CR Geometry: Some Aspects
TL;DR: A survey on some known results, with the addition of some new results, on the geometry of contact semi-Riemannian manifolds of hypersurface type are given, emphasizing similarities and differences with respect to the Riemannia case.
Journal ArticleDOI
The Indefinite Metric of R. Mrugala and the Geometry of the Thermodynamical Phase Space
Serge Preston,James Vargo +1 more
TL;DR: In this article, an indefinite metric G was defined on the contact phase space (P,?) of a homogeneous thermodynamical system and the curvature properties and the isometry group of the metric G were described.
Journal ArticleDOI
Geodesic Ricci solitons on unit tangent sphere bundles
TL;DR: Abbassi and Kowalski as discussed by the authors showed that the geodesic flow is an infinitesimal harmonic transformation if and only if the structure is Sasaki-Einstein.
Journal ArticleDOI
Symplectic, complex and Kähler structures on four-dimensional generalized symmetric spaces☆
TL;DR: In this paper, the full classification of invariant symplectic, (almost) complex and Kahler structures, together with their paracomplex analogues, on four-dimensional pseudo-Riemannian generalized symmetric spaces was obtained.