منابع مشابه
Quasi - Isometric Rigidity for Psl
1. Introduction. Combining the work of many people yields a complete quasi-isometry classification of irreducible lattices in semisimple Lie groups (see [F] for an overview of these results). One of the first general results in this classification is the complete description, up to quasi-isometry, of all nonuniform lattices in semisimple Lie groups of rank 1, proved by R. Schwartz [S1]. He show...
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In the local theory of submanifolds a fundamental but difficult problem is to describe the isometrically deformable isometric immersions f : M → R into Euclidean space with low codimension p if compared to the dimension n ≥ 3 of the Riemannian manifold. Moreover, one would like to understand the set of all possible isometric deformations. Submanifolds in low codimension are generically rigid si...
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The Pick cubic form is a fundamental invariant in the (equi)affine differential geometry of hypersurfaces. We study its role in the affine isometric embedding problem, using exterior differential systems (EDS). We give pointwise conditions on the Pick form under which an isometric embedding of a Riemannian manifold M3 into R4 is rigid. The role of the Pick form in the characteristic variety of ...
متن کاملLectures on quasi-isometric rigidity
Inspiration: Simple noncompact connected Lie groups — Irreducible symmetric spaces of noncompact type (E.Cartan et al). Here there is an essentially 1-1 correspondence between algebraic objects (a Lie group of a certain type) and geometric objects (certain symmetric spaces). Namely, given a Lie group G on constructs a symmetric space X = G/K (K is a maximal compact subgroup of G) and, conversel...
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The early work of Mostow, Margulis and Prasad on rigidity of arithmetic lattices has evolved into a broad use of quasi-isometry techniques in group theory and low dimensional topology. The word metric on a finitely generated group makes it into a metric space which is uniquely determined up to the geometric relation called quasi-isometry, despite the fact that the metric depends on the choice o...
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1978
ISSN: 2156-2261
DOI: 10.1215/kjm/1250522629