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Riemannian Geometry of Contact and Symplectic Manifolds
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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Structures Which are Harmonic with Respect to Walker Metrics
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On alpha-Kenmotsu manifolds satisfying certain conditions.
TL;DR: In this article, the Ricci semi-symmetric fi-Kenmotsu manifolds are derived from almost contact Riemannian manifolds satis- fying some certain conditions.
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Gravitational Chern-Simons and the adiabatic limit
TL;DR: A key observation is that this geometric assumption corresponds exactly to a Kaluza–Klein Ansatz for the metric tensor on the authors' three-manifold, which allows us to translate the problem into the language of general relativity.
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Harmonicity of sections of sphere bundles
TL;DR: In this paper, the energy functional on the space of sections of a sphere bundle over a Riemannian manifold equipped with the Sasaki metric is considered and the characterising condition for critical points is discussed.
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