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Riemannian Geometry of Contact and Symplectic Manifolds
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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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Journal ArticleDOI
Non Existence of Totally Contact Umbilical GCR-Lightlike Submanifolds of Indefinite Cosymplectic Manifolds
TL;DR: In this paper, the existence of GCR-light-like submanifolds of indefinite Cosymplectic manifolds was studied and shown to be non-trivial.
Journal ArticleDOI
η-parallel contact 3-manifolds
Jong Taek Cho,Ji Eun Lee +1 more
TL;DR: In this article, a classification of contact 3-dimensional Riemannian manifolds whose Ricci tensors are parallel is given, and it is shown that the condition of local symmetry is equivalent to the Ricci-parallel condition (rS = 0).
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Almost cosymplectic statistical manifolds
TL;DR: In this article, a characterization theorem and a corollary for the almost cosymplectic statistical manifold with Kaehler leaves were proved and the curvature properties of such a manifold were studied.
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Parabolic Geodesics in Sasakian $3$-Manifolds
TL;DR: In this paper, Lee et al. gave explicit parametrizations for all parabolic geodesics in 3D Sasakian space forms, and gave explicit parameterizations for all geodesic structures.