Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling

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  • Evgenii Proutorov
    Department of Physics, Cherepovets State University, Pr. Lunacharskii 5, Cherepovets 162600, Russia
  • Hiroshi Koibuchi
    National Institute of Technology, Ibaraki College, Nakane 866, Hitachinaka, Ibaraki 312-8508, Japan

説明

<jats:p>We study triangulated surface models with nontrivial surface metrices for membranes. The surface model is defined by a mapping r from a two-dimensional parameter space M to the three-dimensional Euclidean space R 3 . The metric variable g a b , which is always fixed to the Euclidean metric δ a b , can be extended to a more general non-Euclidean metric on M in the continuous model. The problem we focus on in this paper is whether such an extension is well defined or not in the discrete model. We find that a discrete surface model with a nontrivial metric becomes well defined if it is treated in the context of Finsler geometry (FG) modeling, where triangle edge length in M depends on the direction. It is also shown that the discrete FG model is orientation asymmetric on invertible surfaces in general, and for this reason, the FG model has a potential advantage for describing real physical membranes, which are expected to have some asymmetries for orientation-changing transformations.</jats:p>

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  • Axioms

    Axioms 6 (2), 10-, 2017-04-25

    MDPI AG

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