A Theorem on the Affine Transformation Group of a Riemannian Manifold
- 1 October 1955
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 9, 39-41
- https://doi.org/10.1017/s0027763000023266
Abstract
Every Riemannian manifold has a unique affine connection without torsion, which is necessarily invariant by any isometrical transformation of the manifold. However, an affine transformation (i.e., transformation leaving invariant the affine connection) is not necessarily an isometrical transformation. (Consider, for example, the ordinary Euclidean space).Keywords
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