## Differential and Integral Equations

- Differential Integral Equations
- Volume 24, Number 5/6 (2011), 495-504.

### A symmetry result on Reinhardt domains

#### Abstract

We show the following symmetry property of a bounded Reinhardt domain $\Omega$ in $\mathbb{C}^{n+1}$: let $M=\partial\Omega$ be the smooth boundary of $\Omega $ and let $h$ be the Second Fundamental Form of $M$; if the coefficient $h(T,T)$ related to the characteristic direction $T$ is constant then $M$ is a sphere. In the Appendix we state the result from a hamiltonian point of view.

#### Article information

**Source**

Differential Integral Equations, Volume 24, Number 5/6 (2011), 495-504.

**Dates**

First available in Project Euclid: 20 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356018915

**Mathematical Reviews number (MathSciNet)**

MR2809618

**Zentralblatt MATH identifier**

1249.32022

**Subjects**

Primary: 53A05: Surfaces in Euclidean space 32V15: CR manifolds as boundaries of domains

#### Citation

Martino, Vittorio. A symmetry result on Reinhardt domains. Differential Integral Equations 24 (2011), no. 5/6, 495--504. https://projecteuclid.org/euclid.die/1356018915