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 Indexread more
Citations
More filters
Journal ArticleDOI
On slant curves in sasakian 3-manifolds
TL;DR: In this paper, the authors study Lancret type problems for curves in Sasakian 3-manifolds and prove that a curve in Euclidean 3-space is of constant slope if and only if its ratio of curvature and torsion is constant.
Journal ArticleDOI
Nullity conditions in paracontact geometry
TL;DR: In this paper, a complete study of paracontact metric manifolds for which the Reeb vector field of the underlying contact structure satisfies a nullity condition (the condition \eqref{paranullity} below, for some real numbers $% \tilde \kappa$ and $\tilde\mu$) is presented.
Journal ArticleDOI
A Canonical Compatible Metric for Geometric Structures on Nilmanifolds
TL;DR: In this paper, the authors define a left invariant Riemannian metric on N compatible with γ to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature.
Journal ArticleDOI
Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds
TL;DR: In this paper, necessary and sufficient conditions for a three-dimensional contact subriemannian manifold to satisfy the Ricci curvature bound were discovered, which is one of the possible generalizations of Ricci curve bound to more general metric measure spaces.
Journal ArticleDOI
The contact magnetic flow in 3D Sasakian manifolds
TL;DR: In this paper, a geometrical approach to magnetic fields in 3D Riemannian manifold is presented, which allows one to easily tie vector fields and 2-forms.