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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
Magnetic curves in quasi-Sasakian 3-manifolds
TL;DR: In this paper, the authors studied magnetic trajectories corresponding to contact magnetic fields in 3-dimensional quasi-Sasakian manifolds and proved that such magnetic curves are geodesics for a certain linear connection for which all four structure tensor fields are parallel.
Book ChapterDOI
Extrinsic Geometric Flows
Vladimir Rovenski,Paweł Walczak +1 more
TL;DR: Theorem 3.3.1 and 3.2 of as discussed by the authors shows that the first derivative of functionals can be used to show convergence of metrics in a weak sense in the weak sense, which is the key role in proofs of hyperbolic PDEs and the generalized companion matrix.
Journal ArticleDOI
Harmonic almost contact structures via the intrinsic torsion
TL;DR: In this paper, the authors studied the harmonicity of almost contact metric structures and showed conditions relating harmonicity and classes of almost-contact metric structures, and showed that such structures give the absolute minimum energy.
Journal ArticleDOI
Ricci curvature of integral submanifolds of an s-space form
TL;DR: In this article, the Ricci curvature and the squared mean curva-ture of an integral submanifold of an S-space form were used to obtain a basic inequality for equality cases.
Journal ArticleDOI
Bi-paracontact structures and Legendre foliations
TL;DR: In this paper, it was shown that any contact metric manifold whose Reeb vector field belongs to the (κ, μ)-nullity distribution canonically carries an almost bi-paracontact structure.