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arXiv · math-ph/9903018

Gauge theory of disclinations on fluctuating elastic surfaces

E. A. Kochetov·V. A. Osipov
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Abstract

A variant of a gauge theory is formulated to describe disclinations on Riemannian surfaces that may change both the Gaussian (intrinsic) and mean (extrinsic) curvatures, which implies that both internal strains and a location of the surface in R^3 may vary. Besides, originally distributed disclinations are taken into account. For the flat surface, an extended variant of the Edelen-Kadic gauge theory is obtained. Within the linear scheme our model recovers the von Karman equations for membranes, with a disclination-induced source being generated by gauge fields. For a single disclination on an arbitrary elastic surface a covariant generalization of the von Karman equations is derived.

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E. A. Kochetov, V. A. Osipov. 1999-03-09. Gauge theory of disclinations on fluctuating elastic surfaces. https://doi.org/10.1088/0305-4470%2F32%2F10%2F013

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