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arXiv · 2606.16654

Comparison theorems in centro-affine differential geometry

Yasuaki Fujitani
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Abstract

For weighted manifolds with Bakry-\'{E}mery Ricci curvature bounded from below, comparison geometric results have been established. The Bakry-\'{E}mery Ricci curvature depends on the effective dimension $N$. In this paper, the case $N = 1$ is further studied in the setting of centro-affine differential geometry. Several examples, such as rotationally symmetric ellipsoids and hyperboloids, arise in rigidity phenomena of comparison theorems.

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Yasuaki Fujitani. 2026-06-15. Comparison theorems in centro-affine differential geometry. https://arxiv.org/abs/2606.16654

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