On the geometric rank of homogeneous spaces of nonpositive curvature

1993 ◽  
Vol 112 (1) ◽  
pp. 151-170 ◽  
Author(s):  
Jens Heber
Keyword(s):  
Homogeneous Spaces ◽  
Nonpositive Curvature ◽  
Geometric Rank

scholarly journals Minimal orbits at infinity in homogeneous spaces of nonpositive curvature

1992 ◽  
Vol 156 (2) ◽  
pp. 287-296 ◽  
Author(s):  
María Josefina Druetta de Martinez
Keyword(s):  
Homogeneous Spaces ◽  
Nonpositive Curvature

HOMOGENEOUS SPACES OF NONPOSITIVE CURVATURE AND THEIR GEODESIC FLOW

1995 ◽  
Vol 06 (02) ◽  
pp. 279-296 ◽  
Author(s):  
JENS HEBER
Keyword(s):  
Homogeneous Space ◽  
Tangent Bundle ◽  
Geodesic Flow ◽  
Homogeneous Spaces ◽  
Nonpositive Curvature ◽  
Partial Classification ◽  
Higher Rank ◽  
Unit Tangent Bundle ◽  
Volume Preserving

Consider the geodesic flow on the unit tangent bundle SH of a 1-connected, irreducible homogeneous space H of nonpositive curvature. We prove that any flow invariant, isometry invariant C0-function on SH is necessarily constant, unless H is symmetric of higher rank. As the main applications, we obtain rigidity and partial classification results for spaces H whose geodesic symmetries are (asymptotically) volume-preserving.

Application of Morse theory to some homogeneous spaces

1969 ◽  
Vol 21 (3) ◽  
pp. 343-353 ◽  
Author(s):  
S. Ramanujan
Keyword(s):  
Morse Theory ◽  
Homogeneous Spaces

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

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