4 citations · 7 across the 7 of their papers we have counts for
7 papers · 1 filter
Attached Submanifolds Beyond Symmetric Spaces
Megan M. Kerr, Tracy L. Payne
We study submanifold geometry in the presence of symmetry, focusing on submanifolds of solvmanifolds with an unusual property relative to Ricci curvature. We generalize work of H.…
A different perspective on H-like Lie algebras
Cathy Kriloff, Tracy Payne
We characterize H-like Lie algebras in terms of subspaces of cones over conjugacy classes in , translating the classification problem for H-like Lie al…
Uniform Lie Algebras and Uniformly Colored Graphs
Tracy L. Payne, Matthew Schroeder
Uniform Lie algebras are combinatorially defined two-step nilpotent Lie algebras which can be used to define Einstein solvmanifolds. These Einstein spaces often have nontrivial iso…
The topology of the set of nonsoliton Lie algebras in the moduli space of nilpotent Lie algebras
Tracy L. Payne
A Lie algebra is called nonsoliton if it does not admit a soliton inner product. We demonstrate that the subset of nonsoliton Lie algebras in the moduli space of indecomposable n-d…
Ricci flow on three-dimensional, unimodular metric Lie algebras
David Glickenstein, Tracy L. Payne
We give a global picture of the Ricci flow on the space of three-dimensional, unimodular, nonabelian metric Lie algebras considered up to isometry and scaling. The Ricci flow is vi…
The Ricci Flow for Nilmanifolds
Tracy L. Payne
We consider the Ricci flow for simply connected nilmanifolds, which translates to a Ricci flow on the space of nilpotent metric Lie algebras. We consider the evolution of the inner…