Riemannian manifolds of dimension 7 whose skew-symmetric curvature operator has constant eigenvalues

Y. Nikolayevsky

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arXiv · math/0311429

Riemannian manifolds of dimension 7 whose skew-symmetric curvature operator has constant eigenvalues

Y. Nikolayevsky

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Abstract

A Riemannian manifold is called IP, if the eigenvalues of its skew-symmetric curvature operator are pointwise constant. It was previously shown that for all n\ge 4, except n=7, any IP manifold either has constant curvature, or is a warped product, with some specific function, of a line and a space of constant curvature. We extend this result to the case n = 7, and also study 3-dimensional IP manifolds.

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Y. Nikolayevsky. 2003-11-28. Riemannian manifolds of dimension 7 whose skew-symmetric curvature operator has constant eigenvalues. https://arxiv.org/abs/math/0311429

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