Einstein extensions of Riemannian manifolds

Abstract: Given a Riemannian space $N$ of dimension $n$ and a field $D$ of symmetric endomorphisms on $N$, we define the extension $M$ of $N$ by $D$ to be the Riemannian manifold of dimension $n+1$ obtained from $N$ by a construction similar to extending a Lie group by a derivation of its Lie algebra. We find the conditions on $N$ and $D$ for $M$ to be Einstein, and then study various classes of Einstein extensions so obtained. It turns out that several remarkable phenomena and properties which were observed in the homogeneous case are still present in the Riemannian case. This is a joint work with D. Alekseevsky.

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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