On some formulas for families of curves and surfaces and Aminov's divergent representations

DOI10.1134/S1995080218010201zbMath1421.53018OpenAlexW2793997168MaRDI QIDQ2412958

A. G. Megrabov

Publication date: 6 April 2018

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1995080218010201

zbMATH Keywords

conservation lawsvector fieldfamily of curvestotal curvaturefamily of surfaces

Mathematics Subject Classification ID

Differential geometric aspects in vector and tensor analysis (53A45) Hyperbolic conservation laws (35L65) Surfaces in Euclidean and related spaces (53A05)

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Conservation laws and other formulas for families of rays and wavefronts and for the eikonal equation ⋮ Numerical analysis of two-dimensional magnetic cloaking problems based on an optimization method

Cites Work

• Divergence formulas (conservation laws) in the differential geometry of plane curves and their applications
• Differential identities relating the modulus and direction of a vector field and Euler's hydrodynamic equations
• Some differential identities and and their applications to the eikonal equation
• Divergence properties of curvatures of a vector field and a family of surfaces
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