scholarly journals A geometric characterization of negatively curved locally symmetric spaces

1991 ◽  
Vol 34 (1) ◽  
pp. 193-221 ◽  
Author(s):  
Ursula Hamenstädt
Keyword(s):  
Symmetric Spaces ◽  
Geometric Characterization ◽  
Locally Symmetric Spaces ◽  
Negatively Curved

A dynamical-geometric characterization of the geodesic flows of negatively curved locally symmetric spaces

2014 ◽  
Vol 35 (7) ◽  
pp. 2094-2113
Author(s):  
YONG FANG
Keyword(s):  
Symmetric Spaces ◽  
Geodesic Flows ◽  
Anosov Flow ◽  
Rigidity Result ◽  
Locally Symmetric Spaces ◽  
Negatively Curved ◽  
Finite Covers ◽  
Constant Change ◽  
Rank One

In this paper we prove the following rigidity result: let ${\it\varphi}$ be a $C^{\infty }$ topologically mixing transversely symplectic Anosov flow. If (i) its weak stable and weak unstable distributions are $C^{\infty }$ and (ii) its Hamenstädt metrics are sub-Riemannian, then up to finite covers and a constant change of time scale, ${\it\varphi}$ is $C^{\infty }$ flow conjugate to the geodesic flow of a closed locally symmetric Riemannian space of rank one.

scholarly journals Smooth and PL-rigidity problems on locally symmetric spaces

2016 ◽  
Vol 7 (4) ◽  
pp. 205
Author(s):  
Ramesh Kasilingam
Keyword(s):  
Symmetric Spaces ◽  
Riemannian Metrics ◽  
Teichmüller Space ◽  
Teichmuller Space ◽  
Topological Properties ◽  
Open Problems ◽  
Locally Symmetric Spaces ◽  
Negatively Curved ◽  
Rigidity Problems

This is a survey on known results and open problems about smooth and PL-rigidity problem for negatively curved locally symmetric spaces. We also review some developments about studying the basic topological properties of the space of negatively curved Riemannian metrics and the Teichmuller space of negatively curved metrics on a manifold.

scholarly journals THE STRUCTURE OF HARMONIC MORPHISMS WITH TOTALLY GEODESIC FIBRES

2004 ◽  
Vol 06 (03) ◽  
pp. 419-430 ◽  
Author(s):  
M. T. MUSTAFA
Keyword(s):  
Riemannian Manifolds ◽  
Symmetric Spaces ◽  
Positive Curvature ◽  
Compact Manifolds ◽  
Harmonic Morphisms ◽  
Compact Type ◽  
Riemannian Submersions ◽  
Locally Symmetric Spaces ◽  
Totally Geodesic ◽  
Negatively Curved

The structure of local and global harmonic morphisms between Riemannian manifolds, with totally fibres, is investigated. It is shown that non-positive curvature of the domain obstructs the existence of global harmonic morphisms with totally geodesic fibres and the only such maps from compact Riemannian manifolds of non-positive curvature are, up to a homothety, totally geodesic Riemannian submersions. Similar results are obtained for local harmonic morphisms with totally geodesic fibres from open subsets of non-negatively curved compact and non-compact manifolds. During the course, we prove non-existence of submersive harmonic morphisms with totally geodesic fibres from some important domains, for instance from compact locally symmetric spaces of non-compact type and open subsets of symmetric spaces of compact type.

scholarly journals Lp spectral theory and heat dynamics of locally symmetric spaces

2010 ◽  
Vol 258 (4) ◽  
pp. 1121-1139 ◽  
Author(s):  
Lizhen Ji ◽  
Andreas Weber
Keyword(s):  
Spectral Theory ◽  
Symmetric Spaces ◽  
Locally Symmetric Spaces
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