scholarly journals Metrics with prescribed Ricci curvature on homogeneous spaces

2016 ◽  
Vol 106 ◽  
pp. 275-283 ◽  
Author(s):  
Artem Pulemotov
Keyword(s):  
Ricci Curvature ◽  
Homogeneous Spaces

scholarly journals Prescribing Ricci curvature on homogeneous spaces

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Jorge Lauret ◽  
Cynthia E. Will
Keyword(s):  
Homogeneous Space ◽  
Ricci Curvature ◽  
Homogeneous Spaces ◽  
Main Tool ◽  
Moment Map ◽  
Invariant Metrics ◽  
Variety Of Algebras ◽  
Compact Case ◽  
The Moment ◽  
Curvature Problem

Abstract The prescribed Ricci curvature problem in the context of G-invariant metrics on a homogeneous space M = G / K {M=G/K} is studied. We focus on the metrics at which the map g ↦ Rc ⁡ ( g ) {g\mapsto\operatorname{Rc}(g)} is, locally, as injective and surjective as it can be. Our main result is that such property is generic in the compact case. Our main tool is a formula for the Lichnerowicz Laplacian we prove in terms of the moment map for the variety of algebras.

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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