Title: Translation surfaces and isotropic nets on rational minimal surfaces
Authors: Vršek, Jan
Lávička, Miroslav
Citation: VRŠEK, J., LÁVIČKA, M. Translation surfaces and isotropic nets on rational minimal surfaces. 9th International Conference, MMCS 2016, Oslo, Tonsberg, June 23 - June 28, 2016, Revised Selected Papers. Heidelberg: Springer, 2017. s. 186-201. ISBN 978-3-319-67885-6.
Issue Date: 2017
Publisher: Springer
Document type: preprint
URI: http://hdl.handle.net/11025/29271
ISBN: 978-3-319-67885-6
Keywords: translační povrch;algebraické povrchy;stupňovitý vzorec;racionální minimální plochy
Keywords in different language: Translation surfaces;algebraic surfaces;degree formula;rational minimal surfaces
Abstract in different language: We will deal with the translation surfaces which are the shapes generated by translating one curve along another one. We focus on the geometry of translation surfaces generated by two algebraic curves in space and study their properties, especially those useful for geometric modelling purposes. It is a classical result that each minimal surface may be obtained as a translation surface generated by an isotropic curve and its complex conjugate. Thus, we can study the minimal surfaces as special instances of translation surfaces. All the results about translation surfaces will be directly applied also to minimal surfaces. Finally, we present a construction of rational isotropic curves with a prescribed tangent field which leads to the description of all rational minimal surfaces. A close relation to surfaces with Pythagorean normals will be also discussed.
Rights: Plný text je přístupný v rámci univerzity přihlášeným uživatelům.
© Springer Verlag
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