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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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Contact hypersurfaces and CR-symmetry
TL;DR: In this article, it was shown that the contact metric spaces whose Boeckx invariant is defined as real hypersurfaces of the complex quadric quadratic complex and its non-compact dual are realized as hypersurface in Hermitian symmetric spaces.
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The foliated structure of contact metric $(\kappa,\mu)$-spaces
TL;DR: In this article, a geometrical interpretation of the Boeckx's classification of contact metric $(\kappa,\mu)$-spaces is given and necessary conditions for a contact manifold to admit a compatible contact metric.
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Lightlike Geometry of Leaves in Indefinite Kenmotsu Manifolds
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Ricci Soliton and eta-Ricci Soliton on Generalized Sasakian Space Form
TL;DR: In this article, the authors studied Ricci soliton, eta-Ricci solitons and various types of curvature tensors on Generalized Sasakian space form.
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Gradient Ricci solitons on almost Kenmotsu manifolds
TL;DR: In this article, it was shown that the Ricci soliton of an almost Kenmotsu manifold with conformal Reeb foliation is an Einstein metric and Ricci is expanding with λ = 4n.