Integrable geodesic flows on 2-torus: Formal solutions and variational principle
نویسندگان
چکیده
منابع مشابه
Integrable Geodesic Flows on Surfaces
We propose a new condition א which enables to get new results on integrable geodesic flows on closed surfaces. This paper has two parts. In the first, we strengthen Kozlov’s theorem on non-integrability on surfaces of higher genus. In the second, we study integrable geodesic flows on 2-torus. Our main result for 2-torus describes the phase portraits of integrable flows. We prove that they are e...
متن کاملToric Integrable Geodesic Flows
By studying completely integrable torus actions on contact manifolds we prove a conjecture of Toth and Zelditch that toric integrable geodesic flows on tori must have flat metrics.
متن کاملQuadratically integrable geodesic flows on the torus and on the Klein bottle
1. If the geodesic flow of a metric G on the torus T 2 is quadratically integrable then the torus T 2 isometrically covers a torus with a Liouville metric on it. 2. The set of quadratically integrable geodesic flows on the Klein bottle is described. §
متن کاملHierarchy of Integrable Geodesic Flows
A family of integrable geodesic flows is obtained. Any such a family corresponds to a pair of geodesically equivalent metrics.
متن کاملJacobi vector fields of integrable geodesic flows
We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces (such situation we have, for example, if the geodesic is hyperbolic), then we can construct a fundamental solution of the the Jacobi-Hill equation ü = −K(u)u....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2015
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2014.08.006