Torsion-free Connections with prescribed Curvature

Efrain Basurto-Arzate

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arXiv · 2406.01530

Torsion-free Connections with prescribed Curvature

Efrain Basurto-Arzate

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Abstract

We provide necessary and sufficient conditions for a curvature map $S\colon U\longrightarrow K(\mathfrak{g})$ to arise from the curvature tensor of a torsion-free connection on a sufficiently small $U'\subset U$ by using a suitable power series approach. This torsion-free connection is uniquely given. The curvature map $S$ is used to effectively compute the holonomy of this connection.

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Efrain Basurto-Arzate. 2024-06-03. Torsion-free Connections with prescribed Curvature. https://arxiv.org/abs/2406.01530

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