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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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Journal ArticleDOI
Topology of Co-symplectic/Co-Kähler Manifolds
TL;DR: In this paper, the authors reveal the topology of co-symplectic/co-Kahler manifolds via symplectic/kahler mapping tori and prove the theorem of Theorem 1.
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Structure theorem for compact vaisman manifolds
Liviu Ornea,Misha Verbitsky +1 more
TL;DR: A locally conformally Kahler (l.c.K) manifold is a complex manifold that admits a holomorphic flow acting by non-trivial homotheties on the manifold as mentioned in this paper.
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On the concircular curvature tensor of a contact metric manifold
TL;DR: In this article, the authors classify N(•)-contact metric manifolds which sat- isfy Z(»;X) ¢ Z = 0, Z( «;X] ¢ R = 0 or R(»,X) ǫ = 0.
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Localization for Wilson Loops in Chern-Simons Theory
TL;DR: In this article, the authors consider the problem of expressing the partition function of Chern-Simons theory in terms of the equivariant cohomology of the moduli space of flat connections on a Seifert manifold M, which is the total space of a nontrivial circle bundle over a Riemann surface.
Journal ArticleDOI
Contact manifolds and generalized complex structures
David Iglesias-Ponte,Aïssa Wade +1 more
TL;DR: In this article, the authors give simple characterizations of contact 1-forms in terms of Dirac structures, and they also relate normal almost contact structures to the Dirac structure theory.