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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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On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds
TL;DR: In this paper, the authors studied semi-parallel light-like hypersurfaces of an indefinite Kenmotsu manifold, tangent to the structure vector field, and established the geometrical configuration of such hypersurface.
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Dirac structures and generalized complex structures on
TL;DR: In this paper, Courant and Courant-Jacobi brackets on the stable tangent bundle TM ×R of a differentiable manifold and corresponding Dirac and DiracJacobi structures can be prolonged to TM × R, k > h, by commuting infinitesimal automorphisms.
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Contact Lorentzian manifolds
TL;DR: In this article, contact structures with associated pseudo-Riemannian metrics were studied, emphasizing their relationship and analogies with respect to the Riemannians case, and the present author focused here on contact Lorentzian structures.
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GEOMETRY OF SPIN AND SPIN c STRUCTURES IN THE M-THEORY PARTITION FUNCTION
TL;DR: In this article, the effects of having multiple spin structures on the partition function of the spacetime fields in M-theory were studied and a potential anomaly appeared in the eta invariants upon variation of the spin structure.
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An \eta-Einstein Kenmotsu metric as a Ricci soliton
TL;DR: In this article, it was shown that if the metric of an η-Einstein Kenmotsu manifold is a Ricci soliton, then it is Einstein and the soliton is expanding.