Geometric structures on manifolds and holonomy-invariant metrics

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Let a manifold M have a geometric structure modelled on the pair (G, X) of a Lie group G and a manifold X on which G acts; that is, the universal cover (M) over tilde of M has an immersion dev: (M) over tilde --> X equivariant with respect to the holonomy homomorphism h:pi(1)(M) --> G. If the image of dev intersects an open subset U of X that has a complete h(pi(1)(M))-invariant metric with certain properties, then dev(-1) (U) covers U under dev, and covers an open submanifold of M under the covering map (M) over tilde --> M. This fills the gap in the proofs of the results of Faltings and Goldman on real and complex projective surfaces.
Publisher
WALTER DE GRUYTER CO
Issue Date
1997
Language
English
Article Type
Article
Keywords

REAL PROJECTIVE-STRUCTURES; CONVEX DECOMPOSITIONS; SURFACES

Citation

FORUM MATHEMATICUM, v.9, no.2, pp.247 - 256

ISSN
0933-7741
DOI
10.1515/form.1997.9.247
URI
http://hdl.handle.net/10203/70952
Appears in Collection
MA-Journal Papers(저널논문)
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