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A submanifold of a Riemannian manifold is called a parallel submanifold ifits second fundamental form is parallel with respect to the van derWaerden-Bortolotti connection. From submanifold point of view, parallelsubmanifolds are the simplest Riemannian submanifolds next to totally geodesicones. Parallel submanifolds form an important class of Riemannian submanifoldssince extrinsic invariants of a parallel submanifold do not vary from point topoint. In this paper we provide a comprehensive survey on this important classof submanifolds.

A comprehensive survey on parallel submanifolds in Riemannian and pseudo-Riemannian manifolds