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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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Conformal Vector Fields and Eigenvectors of Laplacian Operator
TL;DR: In this article, the Ricci curvature in the direction of a certain vector field is greater than or equal to (n − 1)λ, forcing the vector field to be isometric to the n-sphere Sn(λ).
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Sasaki–Einstein and paraSasaki–Einstein metrics from (κ,μ)-structures
TL;DR: In this article, it was shown that every contact metric ( κ, μ ) admits a canonical η -Einstein Sasakian or η-Einstein paraSasakian metric.
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Pseudo-Einstein CR-structures on real hypersurfaces in a complex space form
TL;DR: In this article, the Ricci curvature tensor for the generalized Tanaka-Webster connection on the Levi subbundle is proportional to the Levi form, and a classification of pseudo-Einstein Hopf-hypersurfaces in a non-flat complex space form is given.
Posted Content
A survey on geometry of warped product submanifolds
TL;DR: A survey of warped product submanifolds in various ambient manifolds can be found in this paper, where the authors provide a good introduction to warped product manifolds and a useful reference for further research on this vibrant research subject.
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Contact Calabi-Yau manifolds and special Legendrian submanifolds
Adriano Tomassini,Luigi Vezzoni +1 more
TL;DR: In this article, a generalization of Calabi-Yau structures in the context of Sasakian manifolds is considered and deformations of a special class of Legendrian submanifolds are studied.