Einstein submanifolds with flat normal bundle in space forms are holonomic
Differential Geometry
2017-12-18 v1
Abstract
A well-known result asserts that any isometric immersion with flat normal bundle of a Riemannian manifold with constant sectional curvature into a space form is (at least locally) holonomic. In this note, we show that this conclusion remains valid for the larger class of Einstein manifolds. As an application, when assuming that the index of relative nullity of the immersion is a positive constant we conclude that the submanifold has the structure of a generalized cylinder over a submanifold with flat normal bundle.
Keywords
Cite
@article{arxiv.1712.05462,
title = {Einstein submanifolds with flat normal bundle in space forms are holonomic},
author = {M. Dajczer and C. -R. Onti and Th. Vlachos},
journal= {arXiv preprint arXiv:1712.05462},
year = {2017}
}
Comments
To appear in Proc. Amer. Math. Soc