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Skew Minimal Surfaces Supported by Two Triangular Frames

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Abstract

An exact solution is constructed for the problem concerning the configuration of skew minimal surfaces supported by two equilateral triangular frames by applying the Chaplygin transform to hodograph variables. Skew appears due to a special arrangement of frames: they are not coaxial, but have central symmetry with respect to a certain point and mirror symmetry with respect to one of three planes formed by pairs of parallel bisectors belonging to the upper and lower frames. In the particular case of coaxial frames, our solution is compared with the known solution, which was found by the Weierstrass–Enneper representation.

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ACKNOWLEDGMENTS

The author is thankful to K.G. Kornev for useful discussions.

Funding

The work was supported by the Ministry of Science and Higher Education of the Russian Federation under agreement No. 075-15-2020-931 within the framework of the development program for the world-class Research Center “Efficient development of the global liquid hydrocarbon reserves.”

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  1. Kazan Federal University, 420008, Kazan, Russia

    M. M. Alimov

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  1. M. M. Alimov
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Correspondence to M. M. Alimov.

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Translated by E. Glushachenkova

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Alimov, M.M. Skew Minimal Surfaces Supported by Two Triangular Frames. Russ Math. 66, 1–20 (2022). https://doi.org/10.3103/S1066369X22050012

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