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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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Structure group U(n) × 1 in thermodynamics
TL;DR: In the context of contact geometry, the authors showed that the structure group of a tangent bundle can be reduced to the group U(n) × 1, where n is the number of degrees of freedom.
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Einstein metrics and GIT stability
Akito Futaki,Hajime Ono +1 more
TL;DR: In this article, the authors review the problem of finding Einstein metrics on compact K\"ahler manifolds and Sasaki manifolds, and show that the problem fits better with the notion of stability in Geometric Invariant Theory if they extend the problem to that of finding extremal K''ahler metrics or constant scalar curvature K ''ahler metric.
On the existence of generalized quasi-Einstein manifolds
Uday Chand De,Sahanous Mallick +1 more
TL;DR: In this paper, the existence of a generalized quasi-Einstein manifold has been proved by non-trivial examples, which is a type of Riemannian manifold.
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Stability of Riemannian manifolds with Killing spinors
TL;DR: Dai et al. as discussed by the authors proved that all complete Riemannian manifolds with imaginary Killing spinors are (linearly) strictly stable in [Stable and unstable Einstein warped products, preprint (2015), arXiv:1507.01782v1].