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Publicly Available Published by De Gruyter January 16, 2016

Classes of generalized Weingarten surfaces in the Euclidean 3-space

  • Diogo G. Dias EMAIL logo and Armando M. V. Corro
From the journal Advances in Geometry

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.

Received: 2013-9-30
Revised: 2014-5-27
Published Online: 2016-1-16
Published in Print: 2016-1-1

© 2016 by Walter de Gruyter Berlin/Boston

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