Curvature symmetries characterizing Einstein spaces
Volume 152 / 2018
Colloquium Mathematicum 152 (2018), 23-28
MSC: Primary 53C25; Secondary 53B20.
DOI: 10.4064/cm7234-5-2017
Published online: 22 January 2018
Abstract
Singer and Thorpe discovered a symmetry of sectional curvatures which characterizes 4-dimensional Einstein spaces. Later this result was generalized to Einstein spaces of even dimensions $n = 2k \ge 4.$ Our Main Theorem establishes curvature symmetries for Einstein spaces of arbitrary dimension $n \ge 4.$
