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arXiv · 1812.06027

Maximally-warped metrics with harmonic curvature

Andrzej Derdzinski·Paolo Piccione
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Abstract

We describe the local structure of Riemannian manifolds with harmonic curvature which admit a maximum number, in a well-defined sense, of local warped-product decompositions, and at the same time their Ricci tensor has, at some point, only simple eigenvalues. We also prove that, in every given dimension greater than two, the local-isometry types of such manifolds form a finite-dimensional moduli space, and a nonempty open subset of this moduli space is realized by locally irreducible complete metrics which are neither Ricci-parallel, nor -- for dimensions greater than three -- conformally flat.

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Andrzej Derdzinski, Paolo Piccione. 2018-12-14. Maximally-warped metrics with harmonic curvature. https://doi.org/10.1090/conm%2F756%2F15198

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