Torsion-free Connections with prescribed Curvature

2024/06/03 by Basurto-Arzate, Efrain
#53A55 #53B05 #53C29 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.01530

Abstract

We provide necessary and sufficient conditions for a curvature map S\colon U\longrightarrow K(\mathfrakg) to arise from the curvature tensor of a torsion-free connection on a sufficiently small U'⊂ 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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