Automorphisms and a reduction theorem in a Sasakian space form E2m+1(−3)

Summary We construct definitely the automorphism group of a Sasakian space form ¯M=E ^2m+1 (–3) and study the existence of a totally geodesic invariant submanifold of ¯M tangent to a given invariant subspace in the tangent space of ¯M. We also study the Frenet curves in ¯M under a totally contact geodesic immersion of a contact CR-submanifold into ¯M. The purpose of this paper is to prove a reduction theorem of the codimension for a totally contact geodesic, contact CR-submanifold of ¯M.