Inhomogeneous deformations of Einstein solvmanifolds

Adam Thompson

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arXiv · 2305.05923

Inhomogeneous deformations of Einstein solvmanifolds

Adam Thompson

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Abstract

For each non-flat, unimodular Ricci soliton solvmanifold $(\mathsf{S}_0,g_0)$, we construct a one-parameter family of complete, expanding, gradient Ricci solitons that admit a cohomogeneity one isometric action by $\mathsf{S}_0$. The orbits of this action are hypersurfaces homothetic to $(\mathsf{S}_0,g_0)$. These metrics are asymptotic at one end to an Einstein solvmanifold. In the one-parameter family, exactly one metric is Einstein, and exactly one has orbits that are isometric to $(\mathsf{S}_0,g_0)$.

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BibTeX RIS

Adam Thompson. 2023-05-10. Inhomogeneous deformations of Einstein solvmanifolds. https://arxiv.org/abs/2305.05923

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