TY - JOUR
T1 - Rigidity for Einstein Manifolds under Bounded Covering Geometry
AU - Si , Cuifang
AU - Xu , Shicheng
JO - Journal of Mathematical Study
VL - 2
SP - 145
EP - 163
PY - 2025
DA - 2025/06
SN - 58
DO - http://doi.org/10.4208/jms.v58n2.25.02
UR - https://global-sci.org/intro/article_detail/jms/24207.html
KW - Einstein, rigidity, almost nonnegative Ricci curvature, bounded covering geometry, space forms.
AB - <p style="text-align: justify;">In this note, we prove three rigidity results for Einstein manifolds with
bounded covering geometry. (1) An almost flat manifold $(M,g)$ must be flat if it is
Einstein, i.e. ${\rm Ric}_g =λg$ for some real number $λ.$ (2) A compact Einstein manifold with
a non-vanishing and almost maximal volume entropy is hyperbolic. (3) A compact
Einstein manifold admitting a uniform local rewinding almost maximal volume is isometric to a space form.</p>