The Chen invariants of warped products of hyperbolic planes and their applications to immersibility problems

Abstract

The classical obstruction to minimal isometric immersions into Euclidean space is $Ric \geq 0$. In this article we construct examples of Riemannian manifolds with $Ric \lt 0$ which don't admit any minimal isometric immersion into Euclidean space for any codimension, by applying Chen invariants.