scispace - formally typeset
Open AccessBook

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 Index

read more

Content maybe subject to copyright    Report

Citations
More filters
Journal Article

Relative nullity foliations and lightlike hypersurfaces in indefinite Kenmotsu manifolds

TL;DR: In this article, the relative nullity distributions of light-like hypersurfaces of indefinite Kenmotsu space forms, tangent to the structure vector field, were investigated.
Journal ArticleDOI

Some results on (k, μ)′-almost Kenmotsu manifolds

TL;DR: In this paper, the Weyl conformal curvature tensor and concircular curvatures tensor were studied on a (k, μ)′-almost Kenmotsu manifold M2n+1 of dimension greater than 3.
Posted Content

C-totally real warped product submanifolds

TL;DR: In this article, a basic inequality involving the Laplacian of the warping function and the squared mean curvature of any warped product isometrically immersed in a Riemannian manifold without assuming any restriction on the curvature tensor of the ambient manifold was obtained.
Journal ArticleDOI

Magnetic curves in tangent sphere bundles II

TL;DR: In this article, the authors studied contact magnetic curves in the unit tangent sphere bundle over the Euclidean plane, and obtained all contact magnetic curve which are slant, which is a special case of the slant magnetic curves.
Posted Content

Slant Riemannian Submersions from Sasakian Manifolds

TL;DR: In this article, the authors introduce slant Riemannian submersions from Sasakian manifolds onto RiemANNian manifold, and give an example of such submerions.