A Fundamental Theorem of Space-times

TL;DR

This paper extends the fundamental theorem of submanifolds to space-times, revealing that the integrability conditions encompass Einstein and Yang-Mills equations, thus linking geometry with fundamental physics.

Contribution

It adapts the fundamental theorem of submanifolds to space-times and uncovers that integrability conditions include Einstein and Yang-Mills equations.

Findings

Integrability conditions contain Einstein equations

Integrability conditions contain Yang-Mills equations

Links geometry with fundamental physical laws

Abstract

The fundamental theorem of submanifolds is adapted to space-times. It is shown that the integrability conditions for the existence of submanifolds of a pseudo-Euclidean space contain the Einstein and Yang-Mills equations.