Affine connections on involutive G-structures
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Publication:5285036
zbMATH Open0876.53014arXivdg-ga/9509001MaRDI QIDQ5285036
Publication date: 4 February 1997
Abstract: This paper is a review of the twistor theory of irreducible G-structures and affine connections. Long ago, Berger presented a very restricted list of possible irreducibly acting holonomies of torsion-free affine connections. His list was complete in the part of metric connections, while the situation with holonomies of non-metric torsion-free affine connections was and remains rather unclear. One of the results discussed in this review asserts that any torsion-free holomorphic affine connection with irreducibly acting holonomy group can, in principle, be constructed by twistor methods. Another result reveals a new natural subclass of affine connections with "very little torsion" which shares with the class of torsion-free affine connections two basic properties --- the list of irreducibly acting holonomy groups of affine connections in this subclass is very restricted and the links with the twistor theory are again very strong.
Full work available at URL: https://arxiv.org/abs/dg-ga/9509001
Moduli problems for differential geometric structures (58D27) Twistor theory, double fibrations (complex-analytic aspects) (32L25) Global submanifolds (53C40) Connections (general theory) (53C05) (G)-structures (53C10)
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