More exact solutions of the constant astigmatism equation

Hlaváč, Adam

doi:10.1016/j.geomphys.2017.09.003

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2020

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“…For this reason, the Gauss equation of these surfaces is related with the sine-Gordon equation, which is known to be integrable in the sense of the soliton theory. Recently there has been an increasing interest in studying the Gauss equation of these surfaces using the theory of integrable systems: [3,8,9,10,11,17,19]. For our purposes, we need to extend the notion of constant astigmatism surfaces in any 3-dimensional Riemannian space.…”

Section: Introductionmentioning

confidence: 99%

Rotational surfaces of constant astigmatism in space forms

López

Pámpano

2020

Journal of Mathematical Analysis and Applications

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A surface in a Riemannian space is called of constant astigmatism if the difference between the principal radii of curvatures at each point is a constant function. In this paper we give a classification of all rotational surfaces of constant astigmatism in space forms. We also prove that the generating curves of such surfaces are critical points of a variational problem for a curvature energy. Using the description of these curves, we locally construct all rotational surfaces of constant astigmatism as the associated binormal evolution surfaces from the generating curves.

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