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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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Tightness in contact metric 3-manifolds
TL;DR: In this article, the authors studied the relation between Riemannian geometry and global properties of contact structures on 3-manifolds and proved an analog of the sphere theorem in the setting of contact geometry.
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The decomposition of almost paracontact metric manifolds in eleven classes revisited
Simeon Zamkovoy,Galia Nakova +1 more
TL;DR: In this paper, the covariant derivative of the structure tensor field has been used to define the classes of almost paracontact metric manifolds with respect to a Lie group.
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Locally ϕ-symmetric normal almost contact metric manifolds of dimension 3
TL;DR: It is proved that in a three-dimensional normal almost contact metric manifold with α, β = constant if the Ricci tensor is η -parallel, then the manifold is locally ϕ -symmetric.
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Anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds
TL;DR: In this paper, the integrability of the distributions and the geometry of foliations of Riemannian submersions from warped product manifolds onto RiemANNian manifolds are investigated.