Strong Rigidity of Locally Symmetric Spaces
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A01=G. Daniel Mostow
A01=George Daniel Mostow
Addition
Adjoint representation
Affine space
Approximation
Author_G. Daniel Mostow
Author_George Daniel Mostow
Automorphism
Axiom
Big O notation
Boundary value problem
Category=PB
Cohomology
Compact Riemann surface
Compact space
Conjecture
Constant curvature
Corollary
Counterexample
Covering group
Covering space
Curvature
Diameter
Diffeomorphism
Differentiable function
Dimension
Direct product
Division algebra
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Ergodicity
Erlangen program
Existence theorem
Exponential function
Finitely generated group
Fundamental domain
Fundamental group
Geometry
Half-space (geometry)
Hausdorff distance
Hermitian matrix
Homeomorphism
Homomorphism
Hyperplane
Identity matrix
Inner automorphism
Isometry group
Jordan algebra
Matrix multiplication
Metric space
Mobius transformation
Morphism
Normal subgroup
Normalizing constant
Partially ordered set
Permutation
Projective space
Riemann surface
Riemannian geometry
Sectional curvature
Self-adjoint
Set function
Smoothness
Stereographic projection
Subgroup
Subset
Symmetric space
Tangent space
Tangent vector
Theorem
Topology
Tubular neighborhood
Two-dimensional space
Unit sphere
Vector group
Weyl group
Product details
- ISBN 9780691081366
- Weight: 28g
- Dimensions: 152 x 229mm
- Publication Date: 21 Dec 1973
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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Locally symmetric spaces are generalizations of spaces of constant curvature. In this book the author presents the proof of a remarkable phenomenon, which he calls "strong rigidity": this is a stronger form of the deformation rigidity that has been investigated by Selberg, Calabi-Vesentini, Weil, Borel, and Raghunathan. The proof combines the theory of semi-simple Lie groups, discrete subgroups, the geometry of E. Cartan's symmetric Riemannian spaces, elements of ergodic theory, and the fundamental theorem of projective geometry as applied to Tit's geometries. In his proof the author introduces two new notions having independent interest: one is "pseudo-isometries"; the other is a notion of a quasi-conformal mapping over the division algebra K (K equals real, complex, quaternion, or Cayley numbers). The author attempts to make the account accessible to readers with diverse backgrounds, and the book contains capsule descriptions of the various theories that enter the proof.
