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Keywords:
manifold; linear connection; pseudo-Riemannian metric; holonomy group; holonomy algebra
manifold; linear connection; pseudo-Riemannian metric; holonomy group; holonomy algebra
Summary:
We contribute to the following: given a manifold endowed with a linear connection, decide whether the connection arises from some metric tensor. Compatibility condition for a metric is given by a system of ordinary differential equations. Our aim is to emphasize the role of holonomy algebra in comparison with certain more classical approaches, and propose a possible application in the Calculus of Variations (for a particular type of second order system of ODE’s, which define geodesics of a linear connection, components of a metric compatible with the connection play the role of variational multipliers).
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