On the Curvature and Heat Flow on Hamiltonian Systems

Abstract

We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.

Keywords

• hamiltonian
• curvature
• comparison theorem
• heat flow