RIEMANNIAN SUBMANIFOLDS WITH CONCIRCULAR CANONICAL FIELD

Abstract

Let M̃ be a Riemannian manifold equipped with a concircular vector field X̃ and M a submanifold (with its induced metric) of M̃ . Denote by X the restriction of X̃ on M and by XT the tangential component of X, called the canonical field of M . In this article we study submanifolds of M̃ whose canonical field XT is also concircular. Several characterizations and classification results in this respect are obtained.