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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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Riemann solitons and almost Riemann solitons on almost Kenmotsu manifolds
TL;DR: In this paper, the authors studied the Riemann soliton and gradient almost-Riemann-soliton on a certain class of almost Kenmotsu manifolds.
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Geometry of Kaluza–Klein metrics on the sphere {\mathbb{S}^3}
TL;DR: In this paper, a new family of Riemannian metrics on the three-sphere is introduced, which are called the Kaluza-Klein type and are induced in a natural way by the corresponding metrics defined on the tangent sphere bundle.
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The harmonicity of nearly cosymplectic structures
Eric Loubeau,E. Vergara-Diaz +1 more
TL;DR: In this article, the class of nearly cosymplectic almost contact structures on a Rie- mannian manifold and prove curvature identities which imply the harmonicity of their parametrizing section, thus complementing earlier results on nearly- Kahler almost complex structures.
Journal ArticleDOI
Approaches to generalize contact structures
Yat Sun Poon,Aïssa Wade +1 more
TL;DR: In this article, the integrability of almost contact structures from both a Sasakian perspective in terms of a cone construction and from a Courant algebroid perspective is examined.
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Levi-Kahler reduction of CR structures, products of spheres, and toric geometry
TL;DR: In this article, the Levi-Kahler quotient of toric CR manifolds has been studied in arbitrary codimension, and a process called the Levi Kullback quotient is introduced for constructing Kahler metrics from CR structures with a transverse torus action.