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

Abstract

Two types of elementary and direct proofs of the classification theorem for CR automorphisms of generalized ellipsoids by [MM10] are given. The first proof is to use an invariant decomposition of holomorphic tangent bundle, and the second is to use infinitesimal CR automorphisms. The advantages of our proofs are: (1) The conditions on the number n_j of the variables and the exponents m_j in the defining equation are weakened, (2) the proofs are more direct than [MM10], (3) our proofs may be applicable to wider class of hypersurfaces.