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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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Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form
TL;DR: In this article, a conformal Sasakian manifold is introduced and the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi invariant, invariant and almost invariant submanifolds tangent to the Reeb vector field and equality cases are discussed.
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Homogeneous non-degenerate $3$-$(\alpha,\delta)$-Sasaki manifolds and submersions over quaternionic K\"ahler spaces
TL;DR: In this article, it was shown that every $3$-$(\alpha,\delta)$-Sasaki manifold of dimension $4n + 3$ admits a locally defined Riemannian submersion over a quaternionic Kahler manifold of scalar curvature.
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Locally Conformal C6-Manifolds and Generalized Sasakian-Space-Forms
TL;DR: In this paper, an algebraic characterization of generalized Sasakian-space-forms is presented, with particular attention to the k-nullity condition and pointwise constant curvature properties of l.c. C6-manifolds.
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On the Characteristic Foliations of Metric Contact Pairs
Gianluca Bande,Amine Hadjar +1 more
TL;DR: In this article, it was shown that a contact pair on a manifold admits an associated metric for which the two characteristic contact foliations are orthogonal, and the leaves of the characteristic foliation are minimal with respect to these metrics.
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Analysis of Contact Cauchy-Riemann maps I: a priori $C^k$ estimates and asymptotic convergence
Yong-Geun Oh,Rui Wang +1 more
TL;DR: In this article, the authors developed the analysis of a nonlinear elliptic system of equations associated to each given contact triad on a contact manifold, without involving the symplectization process, and established the local a priori $C^k$ coercive pointwise estimates for all $k \geq 2$ in terms of $\|dw\|_{C^0}$ by doing tensorial calculations on contact manifold itself using the contact triads connection introduced by present the authors.