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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
Citations
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Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators
TL;DR: In this article, the authors investigated the local and global theory of contact isotropic realisations of Jacobi manifolds, which are those of minimal dimension, and established a relation between the existence of symplectic and contact isotropy realisations for Poisson manifolds.
Generalized globally framed f-space-forms
TL;DR: In this article, generalized globally framed f-space-forms are introduced and the interrelation with generalized Sasakian and generalized complex space-forms is pointed out and suitable differential equations allow to discuss the constancy of the '-sectional curvatures.
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A generalization of contact metric manifolds
J. H. Kim,J. H. Park,K. Sekigawa +2 more
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Area-stationary and stable surfaces of class $C^1$ in the sub-Riemannian Heisenberg group ${\mathbb H}^1$
Matteo Galli,Manuel Ritoré +1 more
TL;DR: In this article, the authors consider surfaces of class $C^1$ in the sub-Riemannian Heisenberg group and show that the regular part of the surface is foliated by horizontal straight lines.
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Tight Beltrami fields with symmetry.
TL;DR: In this paper, the authors provided a bound for the volume Vol(M) and the curvature, which implies the universal tightness of the contact structure ξ = ker α.