On the non-linear refractive index-curvature relation

Abstract

We formulate a refractive index-curvature relation using the second rank tensor of Ricci curvature. In a fibre bundle geometry, we relate a scalar refractive index to an Abelian (a linear) curvature form. We also formulate the Gauss-Bonnet-Chern theorem using a non-linear refractive index.