Initial value problems on cohomogeneity one manifolds, I

Luigi Verdiani; Wolfgang Ziller

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arXiv · 2412.06058

Initial value problems on cohomogeneity one manifolds, I

Luigi Verdiani·Wolfgang Ziller

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Abstract

We study initial value problems for various geometric equations on a cohomogeneity manifold near a singular orbit. We show that when prescribing the Ricci curvature, or finding solutions to the Einstein and soliton equations, there exist solutions near the singular orbit, unique up to a finite number of constants. In part I we make a special assumption that significantly simplifies the proof, and will solve the general case in Part II.

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BibTeX RIS

Luigi Verdiani, Wolfgang Ziller. 2024-12-08. Initial value problems on cohomogeneity one manifolds, I. https://arxiv.org/abs/2412.06058

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