The surjectivity of the exponential map for certain Lie groups
The results of this paper can be viewed as strengthening and generalizing results of \textit{K. H. Hofmann} and \textit{A. Mukherjea} [Math. Ann. 234, 263-273 (1978; Zbl 0382.22005)] and are also related to earlier results of Dixmier and Saito. The author proves the following theorem (Theorem 2.1): The exponential map is surjective for any connected, non compact centerless, rank 1 simple Lie group. -- The group is found by considering such a group as the connected group of isometries of a non compact symmetric space \(G/K\) of negative curvature. The main theorem (Theorem 3.2) then implies, that for a centerless real semisimple Lie group, whose non compact, non rank 1 simple factors have only one conjugacy class of Cartan subgroups, the exponential map is always surjective.
scientific article; zbMATH DE number 711475