arXiv subjects
Publications and source records attributed to Thomas Jack Munn.
We construct new families of complete minimal submanifolds of codimension two in the non-compact duals to the classical compact Lie groups $\SOC n/\SO n$, $\SLC n/\SU n$ and $\SpC n/\Sp n$.
Let $G$ be a Lie group equipped with a left-invariant Riemannian metric. Let $K$ be a semisimple and normal subgroup of $G$ generating a left-invariant conformal foliation $\F$ of on $G$. We then show that the foliation $\F$ is Riemannian and minimal. This means that locally the leaves of $\F$ are fibres of a harmonic morphism. We also prove that if the metric restricted to $K$ is biinvariant then $\F$ is totally geodesic.
In this note we study $(λ,μ)$-eigenfamilies on compact Riemannian manifolds when $λ= μ$. We show that any compact manifold admitting a $(λ,λ)$-eigenfunction is a mapping torus and that any $(λ,λ)$-eigenfamily is one dimensional. Additionally, we consider generalised eigenfamilies, which can have higher dimension, and relate these to harmonic Riemannian submersions to a torus.
In this work we introduce a new method for manufacturing minimal submanifolds in Riemannian geometry. For this we employ the so called complex-valued eigenfunctions. This is particularly interesting in the cases when the Riemannian ambient manifold is compact.
Let G be a Lie group equipped with a left-invariant semi-Riemannian metric. Let K be a semisimple subgroup of G generating a left-invariant conformal foliation F of codimension two on G. We then show that the foliation F is minimal. This means that locally the leaves of F are fibres of a complex-valued harmonic morphism. In the Riemannian case, we prove that if the metric restricted to K is biinvariant then F is totally geodesic.