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arXiv · 1105.2082

Convergence of homogeneous manifolds

Jorge Lauret
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Abstract

We study in this paper three natural notions of convergence of homogeneous manifolds, namely infinitesimal, local and pointed, and their relationship with a fourth one, which only takes into account the underlying algebraic structure of the homogeneous manifold and is indeed much more tractable. Along the way, we introduce a subset of the variety of Lie algebras which parameterizes the space of all n-dimensional simply connected homogeneous spaces with q-dimensional isotropy, providing a framework which is very advantageous to approach variational problems for curvature functionals as well as geometric evolution equations on homogeneous manifolds.

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Jorge Lauret. 2012-03-02. Convergence of homogeneous manifolds. https://doi.org/10.1112/jlms%2Fjds023

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