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arXiv · 2009.12956

Limit geometry of complete projective special real manifolds

David Lindemann
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Abstract

We study the limit geometry of complete projective special real manifolds. By limit geometry we mean the limit of the evolution of the defining polynomial and the centro-affine fundamental form along certain curves that leave every compact subset of the initial complete projective special real manifold. We obtain a list of possible limit geometries, which are themselves complete projective special real manifolds, and find a lower bound for the dimension of their respective symmetry groups. We further show that if the initial manifold has regular boundary behaviour, every possible limit geometry is isomorphic to $\mathbb{R}_{>0}\ltimes\mathbb{R}^{n-1}$.

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David Lindemann. 2020-09-27. Limit geometry of complete projective special real manifolds. https://arxiv.org/abs/2009.12956

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