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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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IMPACT FACTOR 2016: 0.552

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Online
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1615-7168
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Volume 16, Issue 1 (Jan 2016)

Issues

Classes of generalized Weingarten surfaces in the Euclidean 3-space

Diogo G. Dias
  • Corresponding author
  • Instituto Federal de Educação, Ciência e Tecnologia de Goiás, CEP 74968-755 - Aparecida de Goiânia-GO, Brazil
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/ Armando M. V. Corro
Published Online: 2016-01-16 | DOI: https://doi.org/10.1515/advgeom-2015-0040

Abstract

We present surfaces with prescribed normal Gaussmap. These surfaces are obtained as the envelope of a sphere congruencewhere the other envelope is contained in a plane. We introduce classes of surfaces that generalize linear Weingarten surfaces, where the coefficients are functions that depend on the support function and the distance function from a fixed point (in short, DSGW-surfaces). The linear Weingarten surfaces, Appell’s surfaces and Tzitzeica’s surfaces are all DSGW-surfaces. From them we obtain new classes of DSGWsurfaces applying inversions, dilatations and parallel surfaces. For a special class of DSGW-surfaces, which is invariant under dilatations and inversions, we obtain a Weierstrass type representation (in short, EDSG Wsurfaces). As applications we classify the EDSGW-surfaces of rotation and present a 2-parameter family of complete cyclic EDSGW-surfaces with an isolated singularity and foliated by non-parallel planes.

Keywords: Generalized Weingarten surfaces; prescribed normal Gauss map,Weierstrass type representation

About the article

Received: 2013-09-30

Revised: 2014-05-27

Published Online: 2016-01-16

Published in Print: 2016-01-01


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2015-0040.

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© 2016 by Walter de Gruyter Berlin/Boston. Copyright Clearance Center

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