Split rank and semisimple automorphism groups of \(G\)-structures
It is proved that if \(H\) is a semisimple Lie group with finite center acting smoothly on a compact manifold \(M\) and preserving a \(G\)-structure on \(M\), where \(G\) is a real algebraic group, then the \(\mathbb R\)-rank of \(H\) is less than or equal to the \(\mathbb R\)-rank of \(G\). The theorem and in fact a stronger assertion was proved earlier (by the same author) under the additional condition that \(H\) defines a volume density.
scientific article; zbMATH DE number 4049899