4-dimensional Space forms as determined by the volumes of small geodesic balls
Differential Geometry
2024-04-25 v1
Abstract
Gray-Vanhecke conjectured that the volumes of small geodesic balls could determine if the manifold is a space form, and provided a proof for the compact 4-dimensional manifold, and some cases. In this paper, similar results for the 4-dimensional case are obtained, based upon tensor calculus and classical theorems rather than the topological characterizations in [6].
Cite
@article{arxiv.2404.15665,
title = {4-dimensional Space forms as determined by the volumes of small geodesic balls},
author = {JeongHyeong Park},
journal= {arXiv preprint arXiv:2404.15665},
year = {2024}
}
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6 pages