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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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Lightlike Hypersurfaces in Indefinite Trans-Sasakian Manifolds
TL;DR: In this paper, the geodesibility of light-like hypersurfaces of indefinite trans-Sasakian manifolds of type (α, β), tangent to the structure vector field, has been established.
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Locally conformally symplectic reduction
Miron Stanciu,Miron Stanciu +1 more
TL;DR: In this paper, the authors present a reduction procedure for locally conformally symplectic (LCS) manifolds with an action of a Lie group preserving the conformal structure, with respect to any regular value of the momentum mapping.
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Complete stable CMC surfaces with empty singular set in Sasakian sub-Riemannian 3-manifolds
TL;DR: For constant mean curvature surfaces of class $C^2$ immersed inside Sasakian sub-Riemannian 3-manifolds, this paper obtained a formula for the second derivative of the area which involves horizontal analytical terms, the Webster scalar curvature of the ambient manifold, and the extrinsic shape of the surface.
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Bi-slant submanifolds of para Hermitian manifolds
Pablo Alegre,Alfonso Carriazo +1 more
TL;DR: In this article, the notion of bi-slant submanifolds of a para Hermitian manifold is introduced and a gallery of examples of such sub-mansions is presented.
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Chen inequalities for submanifolds of a cosymplectic space form with a semi-symmetric metric connection
Cihan Özgür,Cengizhan Murathan +1 more
TL;DR: In this paper, Chen inequalities for submanifolds of a cosym-plectic space form of constant φ-sectional curvature N 2m+1 (c) endowed with a semi-symmetric metric connection are proved.