A characterization of four-dimensional Einstein manifolds

Yi Ching Yen
1973 Proceedings of the American Mathematical Society  
It is shown that for any P on a four-dimensional Einstein manifold M, there exists an orthonormal basis {Y,} in T"(M) such that all the sectional curvatures K( Y(, Y,) are equal.
doi:10.1090/s0002-9939-1973-0332096-3 fatcat:xwdjrnsoxbc75dp76ntctanwci