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Riemannian Geometry of Contact and Symplectic Manifolds
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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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Geometric Inequalities for Warped Products in Riemannian Manifolds
Bang-Yen Chen,Adara M. Blaga +1 more
TL;DR: A comprehensive survey of warped product submanifolds can be found in this article, which is closely related with this inequality, done during the last two decades, and many papers have been published by various geometers.
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The harmonicity of the Reeb vector field with respect to Riemannian g-natural metrics
TL;DR: In this article, it was shown that a 3-dimensional non-Sasakian contact metric manifold is H-contact if and only if (m, g ) is 2-stein.
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On quasi-hemi-slant riemannian maps
TL;DR: In this paper, a necessary and sufficient condition for proper quasi-hemi-slant Riemannian maps to be totally geodesic is given, and structured concrete examples for this notion are given.
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On Willmore Legendrian surfaces in $$\mathbb {S}^5$$ and the contact stationary Legendrian Willmore surfaces
TL;DR: In this paper, Luo et al. used an equality proved in Luo's paper to get a relation between Willmore Legendrian surfaces and contact stationary Legendrian surface and then they used this relation to prove a classification result for willmore geodesic spheres in 6D Sasakian manifolds.