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

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*Peter B. Gilkey*

**E-mail:** gilkey@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. 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