Mathematical Physics

    

On the Refractive Index-Curvature Relation

Authors: Miftachul Hadi

In a two-dimensional space, a refractive index-curvature relation is formulated using the second rank tensor of Ricci curvature. A scalar refractive index describes an isotropic linear optics. In a fibre bundle geometry, a scalar refractive index is related to an Abelian (a linear) curvature form. The Gauss-Bonnet-Chern theorem is formulated using a scalar refractive index. Because the Euler-Poincare characteristic is the topological invariant then a scalar refractive index is also a topological invariant.

Comments: Written in English, 4 pages, no figure.

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Submission history

[v1] 2022-02-19 21:45:17
[v2] 2022-03-26 16:39:27

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