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Curras - Bosch C.
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دانلود کتاب A x -operator on complete riemannian manifolds
by Curras - Bosch C.|
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عنوان فارسی: -operator X در manifolds کامل ریمانی |
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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 [6], [5] or [7]) 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"
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