On 2-stein submanifolds in space forms

TL;DR

This paper proves that certain 2-stein submanifolds in space forms have constant curvature under specific conditions related to their normal connection or codimension.

Contribution

It establishes the constancy of curvature for 2-stein submanifolds in space forms with flat normal connection or low codimension, extending geometric understanding.

Findings

2-stein submanifolds with flat normal connection have constant curvature

Submanifolds with codimension at most 2 have constant curvature

Results extend previous curvature classification in space forms

Abstract

We prove that a 2-stein submanifold in a space form whose normal connection is flat or whose codimension is at most 2, has constant curvature.