Some formulas in a riemannian space
Manindra Chandra Chaki (1956)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Some formulas in a riemannian space
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Classification of locally homogeneous affine connections in two dimensions is a nontrivial problem. (See [] and [] for two different versions of the solution.) Using a basic formula by B. Opozda, [], we prove that all locally homogeneous torsion-less affine connections defined in open domains of a 2-dimensional manifold depend essentially on at most 4 parameters (see Theorem 2.4).