Riemannian manifolds whose skew-symmetric curvature operator has constant eigenvalues II

Peter B. Gilkey

Abstract. A Riemannian metric on a manifold is said to be IP if the eigenvalues of the skew-symmetric curvature operator are pointwise constant, i.e. they depend upon the point of the manifold but not upon the particular $2$ plane in the tangent bundle at that point. The IP metrics for manifolds of dimension $m\ge4$ and $m\ne7,8$ were classified previously; the cases $m=7$ and $m=8$ are exceptional. In this paper, we use somewhat different techniques to classify IP metrics if $m=8$.

AMSclassification. 53B20

Keywords. Curvature operator, $K$ theory