Home » Strong Rigidity of Locally Symmetric Spaces by G. Daniel Mostow
Strong Rigidity of Locally Symmetric Spaces G. Daniel Mostow

Strong Rigidity of Locally Symmetric Spaces

G. Daniel Mostow

Published December 21st 1973
ISBN : 9780691081366
Paperback
204 pages
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 About the Book 

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 beenMoreLocally 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. Cartans symmetric Riemannian spaces, elements of ergodic theory, and the fundamental theorem of projective geometry as applied to Tits 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.