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Solving via Modular Methods Read chapter Read first chapter

2014 | OriginalPaper | Chapter

An Invitation to Quasihomogeneous Rigid Geometric Structures

Author : Sorin Dumitrescu

Published in: Bridging Algebra, Geometry, and Topology

Publisher: Springer International Publishing

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Abstract

This is a survey paper dealing with quasihomogeneous geometric structures, in the sense that they are locally homogeneous on a nontrivial open set, but not on all of the manifold. Our motivation comes from Gromov’s open-dense orbit theorem which asserts that if the pseudogroup of local automorphisms of a rigid geometric structure acts with a dense orbit, then this orbit is open. Fisher conjectured that the maximal open set of local homogeneity is all of the manifold as soon as the following three conditions are fulfilled: the automorphism group of the manifold acts with a dense orbit, the geometric structure is a G-structure (meaning that it is locally homogeneous at the first order) and the manifold is compact. In a recent joint work, with Adolfo Guillot, we succeeded to prove Fisher’s conjecture for real analytic torsion free affine connections on surfaces: we construct and classify those connections which are quasihomogeneous; their automorphism group never act with a dense orbit.

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previous chapter Hodge Invariants of Higher-Dimensional Analogues of Kodaira Surfaces
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Metadata
Title
An Invitation to Quasihomogeneous Rigid Geometric Structures
Author
Sorin Dumitrescu
Copyright Year
2014
Book
Bridging Algebra, Geometry, and Topology

Print ISBN: 978-3-319-09185-3

Electronic ISBN: 978-3-319-09186-0

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-09186-0_7

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