Symmetry groups of solvmanifolds

Abstract: Although it is generally difficult to determine the full isometry group of a solvmanifold $S$, partial knowledge of its symmetries can yield useful information. For example, the existence of a maximally symmetric metric is related to the existence of extensions of the Lie algebra $\mathfrak{s}$ of $S$ which admit a nontrivial Levi decomposition. Motivated by this, we describe the decompositions $\mathfrak{s} = \mathfrak{s}_1 \ltimes \mathfrak{s}_2$ which yield such extensions and develop a procedure for determining their existence. When the step-size of the nilradical of $\mathfrak{s}$ is bounded, we use the representation theory of real semisimple Lie algebras to describe the structure of such extensions. This is joint work with Michael Jablonski.

differential geometry

Audience: researchers in the topic

( video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Riemannian geometry.

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