Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isometries, rigidity, and universal covers   We classify all closed, aspherical Riemannian manifolds M whose universal
cover has indiscrete isometry group. One sample application is the theorem that
any such M with word-hyperbolic fundamental group must be isometric to a
negatively curved, locally symmetric manifold. Another application is the
classification of all contractible Riemannian manifolds covering both compact
and (noncompact, complete) finite volume manifold. There are also applications
to the Hopf Conjecture, a new proof of Kazhdan's Conjecture (Frankel's Theorem)
in complex geometry, etc.
  Ideas in the proof come from Lie theory, the homological theory of
transformation groups, harmonic maps, and large-scale geometry. An extension to
the non-aspherical case is also given.

25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga