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Riemannian Geometry of Contact and Symplectic Manifolds
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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ON N(k)¡QUASI EINSTEIN MANIFOLD
TL;DR: In this paper, an N(k)-quasi-Einstein manifold with constant associated scalars is studied and it is shown that the generator of the manifold is a Killing vector Fleld.
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Ricci tensors on three-dimensional almost coKähler manifolds
TL;DR: In this paper, the Ricci curvature of the Reeb vector field is invariant to the Riemannian curvature tensor in a 3D almost co-Kahler manifold.
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Almost contact metric manifolds whose Reeb vector field is a harmonic section
TL;DR: In this article, the authors investigated almost contact metric manifolds whose Reeb vector field is a harmonic unit vector field, equivalently a harmonic section, and constructed a large class of locally conformal almost cosymplectic manifolds where the associated almost contact metrics σ are harmonic sections, in the sense of Vergara-Diaz and Wood [25] and in some cases they are also harmonic maps.
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Contact metric $(\kappa,\mu)$-spaces as bi-Legendrian manifolds
TL;DR: In this paper, the authors regard a contact metric manifold whose Reeb vector field belongs to the $(\kappa,\mu)$-nullity distribution as a bi-Legendrian manifold and study its canonical bi-legendrian structure.
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A study of three-dimensional paracontact (κ̃,μ̃,ν̃)-spaces
TL;DR: In this paper, a study of three-dimensional paracontact metric (κ,μ,ν)-manifolds whose Reeb vector field ξ is harmonic is presented.