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JOURNALS // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika // Archive

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2025 Number 2, Pages 29–36 (Mi vmumm4669)

Mathematics

Isotermic coordinate system on surfaces of revolution

I. Kh. Sabitov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A method for presenting of the metric of surface in its isothermic form is described with a study of analytical properties of the obtained form. A simple formula for the integral Gauss curvature by the first derivatives of the meridian curve at its boundary points is given.

Key words: surface of rotation, metric, presentation in isothermic form, examples, formula for Gauss curvature, behaviour at poles, integral curvature.

UDC: 514.752.43

Received: 30.04.2024

DOI: 10.55959/MSU0579-9368-1-66-2-5



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© Steklov Math. Inst. of RAS, 2025