Submanifolds with constant Moebius curvature and flat normal bundle

TL;DR

This paper classifies certain geometric submanifolds in Euclidean space that have constant Moebius curvature and flat normal bundle, expanding understanding of their structure in differential geometry.

Contribution

It provides a complete classification of isometric immersions with these properties for dimensions n ≥ 5 and 2p ≤ n, a new result in submanifold theory.

Findings

Classification of submanifolds with constant Moebius curvature

Characterization of submanifolds with flat normal bundle

Extension of known results to higher dimensions

Abstract

We classify isometric immersions $f\colon M^{n}\to \mathbb{R}^{n+p}$, $n \geq 5$ and $2p \leq n$, with constant Moebius curvature and flat normal bundle.