Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling
Department of Physics, Cherepovets State University, Pr. Lunacharskii 5, Cherepovets 162600, Russia
National Institute of Technology, Ibaraki College, Nakane 866, Hitachinaka, Ibaraki 312-8508, Japan
Author to whom correspondence should be addressed.
Academic Editors: Emil Saucan and David Gu
Received: 21 March 2017 / Revised: 14 April 2017 / Accepted: 19 April 2017 / Published: 25 April 2017
We study triangulated surface models with nontrivial surface metrices for membranes. The surface model is defined by a mapping
from a two-dimensional parameter space M
to the three-dimensional Euclidean space
. The metric variable
, which is always fixed to the Euclidean metric
, 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.
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Proutorov, E.; Koibuchi, H. Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling. Axioms 2017, 6, 10.
Proutorov E, Koibuchi H. Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling. Axioms. 2017; 6(2):10.
Proutorov, Evgenii; Koibuchi, Hiroshi. 2017. "Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling." Axioms 6, no. 2: 10.
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