## Isometries of a product of Riemannian manifolds

Theorem. Let and be two compact Riemannian manifolds with irreducible holonomy groups. Let . Then

This result seems to be a folklore, probably well known to the specialists, although it is hard to find it in the literature. The only discussion which I managed to find on Mathoverflow contains …

## Chern connections in the context of CR-geometry

This post is a result of several discussions with Rodion Déev.

#### 1. Preliminaries: Chern’s theorem

Fix a complex manifold and a complex vector bundle over . Recall that a structure of holomorphic bundle on is given by an operator

which satisfies -Leibniz identity

and the integrability condition

For the …

## Demystification of the Willmore integrand

The Willmore energy for a surface in Euclidean 3-space is defined as , where is the mean curvature of and its area form. It’s known to be invariant under the conformal transformations (whereas the mean curvature itself is not). White, and later Bryant noticed that the 2-form , where stands …

## A shortcut in Kapovich’s proof of Haupt’s theorem

The Teichmüller space of genus curves carries the Hodge bundle , the total space of which maps into the first cohomology space via the period map (i. e., a holomorphic 1-form maps into its cohomology class). Haupt’s (or Haupt–Kapovich) theorem describes the image in terms of the integral structure on and …