Bundle decomposition and infinitesimal CR automorphism approaches to CR automorphism group of generalized ellipsoids (Q1932486)

The paper is concerned with the classification of all local CR diffeomorphisms of the set of strictly pseudoconvex points of a generalized ellipsoid \[ E=\big\{ Z\in{\mathbb C}^{n+1}~:~ |z_1|^{2m_1}+\ldots+|z_{s }|^{2m_s }+|z_{n+1}|^2=1\big\}, \] where \((z_1,z_2,\ldots z_s)\in {\mathbb C}^{n_1}\times \ldots\times{\mathbb C}^{n_s}={\mathbb C}^{n }\) are groups of variables and the numbers \(m_j, n_j\) are integers satisfying the conditions \(m_j,~n_j>1\) for \(1\leq j\leq s-1\) and \(n_s\geq 0\). It provides two new proofs of a theorem of \textit{R. Monti} and \textit{D. Morbidelli} [J. Math. Soc. Japan 64, No. 1, 153--179 (2012; Zbl 1250.32034)], where all such local CR diffeomorphisms were shown to extend to global biholomorphisms of the bounded domain with bondary \(E\) and to be the composition of four mappings of a given type. These new proofs can also be modified to address the more general case where some \(m_j\) and \(n_j\) are equal to 1.