Нашли опечатку? Выделите ее мышкой и нажмите Ctrl+Enter
Название: A x -operator on complete riemannian manifolds
Автор: Curras - Bosch C.
In this paper we give a generalisation of Kostant's Theorem about the Ax-operator associated to a Killing vector field X on a compact Riemannian manifold. Kostant proved (see ,  or ) that in a compact Riemannian manifold, the (1, 1) skew-symmetric operator A× = Lx-Vx associated to a Killing vector field X lies in the holonomy algebra at each point. We prove that in a complete non-compact Riemannian manifold (M.g) the A×-operator associated to a Killing vector field, with finite global norm, lies in the holonomy algebra at each point. Finally we give examples of Killing vector fields with infinite global norms on non-fiat manifolds such that Ax does not lie in the holonomy algebra at any point