To the contact distribution of a contact manifold we associate Hamiltonian type vector fields, called contact Hamiltonian fields. Their properties are investigated and the existence of such vector fields nowhere tangent to a given submanifold is proved. Time-depending contact Hamiltonian vector fields allow us to define the contact energy whose properties are studied. A class of submanifolds in relation to the study of contact Hamiltonian fields is also analyzed.
The notion of q-bisectional curvature of a Sasakian manifold M is defined. It is proved that if M has lower bounded q-bisectional curvature and contains a compact invariant submanifold tangent to the structure vector field then M is compact. Myers and Frankel type theorems for Sasakian manifolds with lower bounded and positive q-bisectional curvature, respectively, are also given.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.