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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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Supersymmetric Field Theories on Three-Manifolds
TL;DR: In this article, a supersymmetric field theory on Riemannian three-manifolds was constructed based on the rigid limit of new minimal supergravity in three dimensions, which couples to the flatspace supermultiplet containing the R-current and the energy-momentum tensor.
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Canonical connections on paracontact manifolds
TL;DR: In this article it was shown that an almost paracontact structure admits a connection with totally skew-symmetric torsion if and only if the Nijenhuis tensor of the structure is skew symmetric and the defining vector field is Killing.
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Twisted supersymmetric 5D Yang-Mills theory and contact geometry
Johan Kallen,Maxim Zabzine +1 more
TL;DR: In this paper, a twisted version of the N = 1 supersymmetric Yang-Mills theory is defined on a circle bundle over a four dimensional symplectic manifold, and a generalization of the instanton equations to five dimensional contact manifolds is suggested.
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Generalized Sasakian-space-forms
TL;DR: In this paper, generalized Sasakian-space-forms are introduced and studied, by using some different geometric techniques such as Riemannian submersions, warped products or conformal and related transformations.
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Non-Abelian localization for Chern-Simons theory
Chris Beasley,Edward Witten +1 more
TL;DR: In this article, the authors show that the partition function of Chern-Simons theory admits a topological interpretation in terms of the equivariant cohomology of the moduli space of flat connections on a Seifert manifold.