Certain infinitesimal transformation of normal contact metric manifold

Abstract

Introduction. In the previous paper [2], the author studied infinitesimal conformal and projective transformations of normal contact metric manifold. In the present paper, we study certain infinitesimal transformation of normal contact metric manifold and prove the following THEOREM 1. In a normal contact metric manifold, any curvature-preserving infinitesimal transformation is necessarily an infinitesimal isometry. If the above theorem is proved, we have obviously the following THEOREM 2. In a normal contact metric manifold, an infinitesimal affine transformation is necessarily an infinitesimal isometry. THEOREM 3. In a normal contact metric manifold, an infinitesimal homothetic transformation is necessarily an infinitesimal isometry.