Codimension reduction in symmetric spaces

TL;DR

This paper presents a geometric proof of a generalized theorem on reducing the codimension of submanifolds within Riemannian symmetric spaces, extending classical results in differential geometry.

Contribution

It provides a concise geometric proof of a broader codimension reduction theorem applicable to symmetric spaces, enhancing understanding of submanifold geometry.

Findings

Generalized codimension reduction theorem proven

Geometric proof simplifies previous approaches

Applicable to a wide class of symmetric spaces

Abstract

In this paper we give a short geometric proof of a generalization of a well-known result about reduction of codimension for submanifolds of Riemannian symmetric spaces.