Abstract
In this paper, we find a conformal vector field as well as a Killing vector field on a compact real submanifold of the canonical complex space form (C-m, J, < , >). In particular, using immersion psi : M -> C-m of a compact real submanifold M and the complex structure J of the canonical complex space form (C-m, J, < , >), we find conditions under which the tangential component of J psi is a conformal vector field as well as conditions under which it is a Killing vector field. Finally, we obtain a characterization of n-spheres in the canonical complex space form (C-m, J ,< , >).