# Minkowski identities for hypersurfaces in constant sectional curvature manifolds

## TL;DR

This paper presents a new proof of Minkowski identities for hypersurfaces in constant curvature manifolds, utilizing a differential system approach and introducing a position vector field concept.

## Contribution

It offers a novel proof technique for Minkowski identities and develops the notion of a position vector field in this geometric context.

## Key findings

- New proof of Minkowski identities for hypersurfaces
- Introduction of the position vector field concept
- Application of a differential system approach

## Abstract

We give a new proof of the generalized Minkowski identities relating the higher degree mean curvatures of orientable closed hypersurfaces immersed in a given constant sectional curvature manifold. Our methods rely on a fundamental differential system of Riemannian geometry introduced by the author. We develop the notion of position vector field, which lies at the core of the Minkowski identities.