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arXiv · 2509.12542

Failure of Lichnerowicz-type result in parabolic geometries of real rank at least $3$

Toby Aldape
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Abstract

Given a Yamaguchi nonrigid parabolic model geometry $(G,P)$ with $G$ simple of real rank at least $3$, we use techniques developed by Erickson to establish the existence of closed, nonflat, essential, regular, normal Cartan geometries modeled on $(G,P)$. Yamaguchi nonrigidity is a necessary condition for admitting nonflat, regular, normal examples. This rules out Lichnerowicz-type conjectures for these model geometries.

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Toby Aldape. 2025-09-16. Failure of Lichnerowicz-type result in parabolic geometries of real rank at least $3$. https://arxiv.org/abs/2509.12542

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