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Geometric structures invariant to symmetries
symmetric spaces geometric structures Cartan geometries parabolic geometries homogeneous spaces extension functors
2012/7/11
We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Ca...
Automorphisms of geometric structures associated to Coxeter groups
Automorphisms geometric structures associated Coxeter groups
2012/3/1
In this paper, we consider the automorphism groups of the Cayley graph with respect to the Coxeter generators and the Davis complex of an arbitrary Coxeter group. We determine for which Coxeter groups...
Some (non-)elimination results for curves in geometric structures
Some (non-)elimination results curves geometric structures
2010/11/17
Chevaley-Tarski theorem insures that the projection of a constructible set of $\C ^n$ is also a constructible set. In this note we prove that the projection of a finite boolean combination of algebra...
Problems on geometric structures of projective embeddings
geometric structures projective embeddings
2010/10/29
This is a survey of our research on geometric structures of projective embeddings and includes some topics of our talks in several symposia during 1990-99. We clarify our main problem, which is to co...