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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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Generalized ($\kappa,\mu $)-contact metric manifoldswith $\|{grad}\kappa \| =$ constant
TL;DR: In this article, the authors classify the 3-dimensional generalized ($kappa,\mu$)-contact metric manifolds, which satisfy the condition that the vertices of the manifold have vertices whose gradients are at most $const.
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Ricci solitons and contact metric manifolds
TL;DR: In this article, a Ricci soliton with potential vector field V collinear with ξ at each point under different curvature conditions was studied on a contact metric manifold M2n+1(ϕ, ξ, η, g).
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Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds
Luca Rizzi,Pavel Silveira +1 more
TL;DR: For a fat sub-Riemannian structure, the Ricci curvatures in the sense of Agrachev-Zelenko-Li have been introduced in this paper, where the authors prove comparison results for conjugate lengths, Bonnet-Myers type results and Laplacian comparison theorems for the intrinsic sub-Laplacians.
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Five-dimensional K-contact Lie algebras
Giovanni Calvaruso,Anna Fino +1 more
TL;DR: In this paper, a general approach to the study of left-invariant K-contact structures on Lie groups was introduced, and a classification of five-dimensional Sasakian φ-symmetric Lie algebras was provided.