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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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Para-Sasakian geometry in thermodynamic fluctuation theory
TL;DR: In this paper, the authors tie concepts derived from statistical mechanics, information theory and contact Riemannian geometry within a single consistent formalism for thermodynamic fluctuation theory, and derive the concrete relations characterizing the geometry of the thermodynamic phase space stemming from the relative entropy and the Fisher-Rao information matrix.
Journal ArticleDOI
Quaternionic and para-quaternionic CR structure on (4n+3)-dimensional manifolds
TL;DR: In this paper, the notion of quaternionic and para-quaternionic CR structure on a (4n+3)-dimensional manifold M as a triple (ω1,ω2,ω3) of 1-forms such that the corresponding 2-forms satisfy some algebraic relations was defined.
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Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds
Fabrice Baudoin,Jing Wang +1 more
TL;DR: In this paper, curvature dimension inequalities for the sub-Laplacian on contact Riemannian manifolds were studied, and a new condition was proposed to ensure the compactness of the underlying manifold.
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Topology of Locally Conformally Kähler Manifolds with Potential
Liviu Ornea,Misha Verbitsky +1 more
TL;DR: The existence of a potential can be characterized cohomologically as vanishing of a certain cohomology class, called the Bott-Chern class as mentioned in this paper, which includes the Vaisman manifold.
Journal ArticleDOI
Nearly hypo structures and compact Nearly K\"ahler 6-manifolds with conical singularities
TL;DR: In this paper, it was shown that any Sasaki-Einstein 5-manifold defines a nearly K\"ahler structure on the sin-cone of a 6-dimensional nearly K''ahler manifold.