Title: Riemannian manifolds whose skew-symmetric curvature operator
has constant eigenvalues
Authors: Peter B. Gilkey, John V. Leahy, Hal Sadofsky
AMS classification: 53B20
Address: Department of Mathematics, University of Oregon, Eugene, OR 97403.
Email: gilkey@math.uoregon.edu, leahy@math.uoregon.edu,
sadofsky@math.uoregon.edu
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. We classify
the IP metrics for manifolds of dimensions $m=5$, $m=6$, and $m>8$.