Summary and Info
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"
Review and Comments
Rate the Book
A x -operator on complete riemannian manifolds 0 out of 5 stars based on 0 ratings.