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

arXiv1910.08807MaRDI QIDQ6327507

Publication date: 19 October 2019

Abstract: A submanifold of a Riemannian manifold is called a parallel submanifold if its second fundamental form is parallel with respect to the van der Waerden-Bortolotti connection. From submanifold point of view, parallel submanifolds are the simplest Riemannian submanifolds next to totally geodesic ones. Parallel submanifolds form an important class of Riemannian submanifolds since extrinsic invariants of a parallel submanifold do not vary from point to point. In this paper we provide a comprehensive survey on this important class of submanifolds.

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