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Lines of Affine Principal Curvatures of Surfaces in 3-Space

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Abstract

In this work we study the affine principal lines on surfaces in 3-space. We consider the binary differential equation of the affine curvature lines and obtain the topological models of these curves near the affine umbilic points (elliptic and hyperbolic). We also describe the local generic behavior of affine curvature lines at points with double eigenvalues of the affine shape operator and at parabolic points.

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Acknowledgements

The authors are very grateful to the anoynomus referee for the carefully reading and for several useful comments. This work was partially supported by PRONEX/ CNPq/ FAPEG Grant 201710267000508. The first author is supported by the CAPES project Grant Number \(88887.136371/2017-00-465591/2014-0\)-INCT de Matemática, during a post-doctoral period at IME-UFG, Goiânia, Brazil. The second and third authors are fellows of CNPq.

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  1. Instituto de Matemáticas e Estatística, Universidade Federal de Goiás, Goiânia, GO, Brazil

    M. Barajas & R. Garcia

  2. Departamento de Matemática, PUC-Rio, Rio de Janeiro, RJ, Brazil

    M. Craizer

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  1. M. Barajas
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  2. M. Craizer
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  3. R. Garcia
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Correspondence to M. Barajas.

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Barajas, M., Craizer, M. & Garcia, R. Lines of Affine Principal Curvatures of Surfaces in 3-Space. Results Math 75, 32 (2020). https://doi.org/10.1007/s00025-020-1158-9

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