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Locally homogeneous rigid geometric structures on surfaces | | Sorin Dumitrescu
; | | Date: |
23 Jul 2009 | | Abstract: | We study locally homogeneous rigid geometric structures on surfaces. We show
that a locally homogeneous projective connection on a compact surface is flat.
We also show that a locally homogeneous unimodular affine connection on a two
dimensional torus is complete and, up to a finite cover, homogeneous.
Let $
abla$ be a unimodular real analytic affine connection on a real
analytic compact connected surface $M$. If $
abla$ is locally homogeneous on a
nontrivial open set in $M$, we prove that $
abla$ is locally homogeneous on
all of $M$. | | Source: | arXiv, 0907.4072 | | Services: | Forum | Review | PDF | Favorites | |
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