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A symmetry result on Reinhardt domains. (English) Zbl 1249.32022

Reinhardt domains with a smooth boundary in the \((n+1)\)-dimensional complex space are examined. The role of the characteristic direction \(T\) of the boundary \(M\) of the given Reinhardt domain and the splitting of the tangent space of \(M\) are explained. The main result is: If the Second Fundamental Form \(h\) of the boundary surface \(M\) satisfies \(h(T,T)=R\), where \(R\) is a constant, then \(M\) is a sphere, radius of which is equal \(1/R\). A hamiltonian view-point is treated in the Appendix.

MSC:

32V15 CR manifolds as boundaries of domains
53A05 Surfaces in Euclidean and related spaces
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