Isometric immersions with flat normal bundle between space forms

TL;DR

This paper studies isometric immersions of negatively curved space forms into other space forms with flat normal bundles, showing that their second fundamental form exhibits exponential growth.

Contribution

It proves that the second fundamental form of such immersions grows exponentially when the normal bundle is flat.

Findings

Second fundamental form grows exponentially

Immersions with flat normal bundle exhibit specific curvature behavior

Results apply to space forms with negative curvature

Abstract

We investigate the behavior of the second fundamental form of an isometric immersion of a space form with negative curvature into a space form so that the extrinsic curvature is negative. If the immersion has flat normal bundle, we prove that its second fundamental form grows exponentially.