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arXiv · 1406.2672

Intrinsic and Extrinsic curvatures in Finsler-esque spaces

Dawood Kothawala
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Abstract

We consider metrics related to each other by functionals of a scalar field $\varphi(x)$ and it's gradient $\nabla \varphi(x)$, and give transformations of some key geometric quantities associated with such metrics. Our analysis provides useful and elegant geometric insights into the roles of {\it conformal} and {\it non-conformal} metric deformations in terms of intrinsic and extrinsic geometry of $\varphi$-foliations. As a special case, we compare {\it conformal} and {\it disformal} transforms to highlight some non-trivial scaling differences. We also study the geometry of {\it equi-geodesic} surfaces formed by points $p$ at constant geodesic distance $\sigma(p,P)$ from a fixed point $P$, and apply our results to a specific disformal geometry based on $\sigma(p,P)$ which was recently shown to arise in the context of spacetime with a minimal length.

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Dawood Kothawala. 2014-06-10. Intrinsic and Extrinsic curvatures in Finsler-esque spaces. https://doi.org/10.1007/s10714-014-1836-6

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