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arXiv · 1003.1469

Projective vs metric structures

Pawel Nurowski
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Abstract

We present a number of conditions which are necessary for an n-dimensional projective structure (M,[nabla]) to include the Levi-Civita connection nabla of some metric on M. We provide an algorithm, which effectively checks if a Levi-Civita connection is in the projective class and, in the positive, which finds this connection and the metric. The article also provides a basic information on invariants of projective structures, including the treatment via Cartan's normal projective connection. In particular we show that there is a number of Fefferman-like conformal structures, defined on a subbundle of the Cartan bundle of the projective structure, which encode the projectively invariant information about (M,[nabla]).

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Pawel Nurowski. 2010-03-07. Projective vs metric structures. https://doi.org/10.1016/j.geomphys.2011.04.011

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