Holomorphic curvature of infinite dimensional symmetric complex Banach manifolds of compact type.
Homogeneous Randers spaces admitting just two homogeneous geodesics
The existence of a homogeneous geodesic in homogeneous Finsler manifolds was investigated and positively answered in previous papers. It is conjectured that this result can be improved, namely that any homogeneous Finsler manifold admits at least two homogenous geodesics. Examples of homogeneous Randers manifolds admitting just two homogeneous geodesics are presented.
Homogeneous variational problems: a minicourse
A Finsler geometry may be understood as a homogeneous variational problem, where the Finsler function is the Lagrangian. The extremals in Finsler geometry are curves, but in more general variational problems we might consider extremal submanifolds of dimension . In this minicourse we discuss these problems from a geometric point of view.
Homogeneous variational problems and Lagrangian sections
We define a canonical line bundle over the slit tangent bundle of a manifold, and define a Lagrangian section to be a homogeneous section of this line bundle. When a regularity condition is satisfied the Lagrangian section gives rise to local Finsler functions. For each such section we demonstrate how to construct a canonically parametrized family of geodesics, such that the geodesics of the local Finsler functions are reparametrizations.