A note on the dimension of isometry group of a Riemannian manifold

Abstract

In this paper, we obtain some results on the dimension of the isometry group of a Riemannian manifold. In specific dimensions, we give a range which the dimension of an isometry group can not be in. We also give necessary conditions for a manifold to have a free canonical action on some specific manifolds. We give a boundary of the dimension of the full isometry group if the dimension of a manifold is greater or equal to 4.

Keywords

• Isometry groups of riemannian manifolds,noncompact lie groups of transformations

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