Pseudo-Riemann’s quartics in Finsler’s geometry—two-dimensional case

نویسندگان

چکیده

Abstract Finsler’s geometry usually describes an extension of Riemmann’s into a direction-dependent geometric structure. Historically, the well-known Riemann’s quartic length element example served as inspiration for this construction. Surprisingly, covariant Fresnel equation—a fundamental dispersion relation in solid-state electrodynamics—emerges exact same expression. As result, expression can be regarded mathematical representation physical phenomenon. In study, we offer numerous examples that show geometry, even situation positive definite Euclidean signature space, is too restrictive many applications. The strong axioms are violated substantially greater number distinctive subsets spaces having indefinite (Minkowski) signature. We suggest weaker characterization structure based on explicitly calculated two-dimensional examples. tangential vector concept permits singular subsets. Only open manifold’s tangent bundle required to satisfy geometry. demonstrate unique two dimensions and briefly discuss their possible origins.

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ژورنال

عنوان ژورنال: Journal of physics

سال: 2023

ISSN: ['0022-3700', '1747-3721', '0368-3508', '1747-3713']

DOI: https://doi.org/10.1088/1742-6596/2482/1/012007