https://neckpinch.com/authors/cynthia-e-will/New arXiv papers by Cynthia E. Will, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2301.02335/arxiv:2301.02335Thu, 05 Jan 2023 00:00:00 GMTJorge Lauret, Cynthia E. Will — A generalized metric on a manifold M, i.e., a pair (g,H), where g is a Riemannian metric and H a closed 3-form, is a fixed point of the generalized Ricci flow if and only if (g,H) is Bismut Ricci flat: H is g-harmonic and ric(g)=1/4 H_g². On any homogeneous space M=G/K, where G=G₁× G₂ is a compact semisimple Lie group with two simple factors, under some mild assumptions, we exhibit a Bismut Ricci flat G-invariant generalized metric, which is proved to be unique among a 4-parameter space of metrics in many cases, including when K is neither abelian nor semisimple. On the other hand, if K is simple and the standard metric is Einstein on both G₁/π₁(K) and G₂/π₂(K), we give a one-parameter family of Bismut Ricci flat G-invariant generalized metrics on G/K and show that it is most likely pairwise non-homothetic by computing the ratio of Ricci eigenvalues. This is proved to be the case for every space of the form M=G× G/ΔK and for M³⁵=SO(8)× SO(7)/G₂. A Corrigendum has been added in Appendix A.Ricci flowGeneralized & G₂ flowsRicci-flat & Calabi–YauSmale conjecture & diffeomorphismsHomogeneous spacesEigenvalues & spectrum