Bang-Yen Chen, Shihshu Walter Wei Michigan State University; University of Oklahoma
Abstract : Let $\tilde M$ be a Riemannian manifold equipped with a concircular vector field $\tilde X$ and $M$ a submanifold (with its induced metric) of $\tilde M$. Denote by $X$ the restriction of $\tilde X$ on $M$ and by $X^T$ the tangential component of $X$, called the canonical field of $M$. In this article we study submanifolds of $\tilde M$ whose canonical field $X^T$ is also concircular. Several characterizations and classification results in this respect are obtained.