Classes of generalized Weingarten surfaces in the Euclidean 3-space
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.
- Location
-
Deutsche Nationalbibliothek Frankfurt am Main
- Extent
-
Online-Ressource
- Language
-
Englisch
- Bibliographic citation
-
Classes of generalized Weingarten surfaces in the Euclidean 3-space ; volume:16 ; number:1 ; year:2016 ; pages:45-55 ; extent:11
Advances in geometry ; 16, Heft 1 (2016), 45-55 (gesamt 11)
- Creator
-
Dias, Diogo G.
Corro, Armando M. V.
- DOI
-
10.1515/advgeom-2015-0040
- URN
-
urn:nbn:de:101:1-2024022213291329444943
- Rights
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
-
14.08.2025, 10:46 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Dias, Diogo G.
- Corro, Armando M. V.
Other Objects (12)
Solutions of the Generalized Weierstrass Representation in Four-Dimensional Euclidean Space
A new extragradient method for generalized variational inequality in Euclidean space
THE POLAR GEODESIC COORDINATE SYSTEM ON SURFACES IN THE EUCLIDEAN 3-DIMENSIONAL SPACE
Hardy spaces on the Euclidean space
Higher order rectifiability in Euclidean space
SIMILARITY PROPERTIES WHICH CHARACTERIZE EUCLIDEAN SPACE
Simple factor dressing and the López–Ros deformation of minimal surfaces in Euclidean 3-space
Holographic calculations of Euclidean Wilson loop correlator in Euclidean anti-de Sitter space
Geometric probabilities in the Euclidean space E3
Normal curves in n-dimensional Euclidean space
Some hemivariational inequalities in the Euclidean space
Framed slant helices in Euclidean 3-space
Solutions of the Generalized Weierstrass Representation in Four-Dimensional Euclidean Space
A new extragradient method for generalized variational inequality in Euclidean space
THE POLAR GEODESIC COORDINATE SYSTEM ON SURFACES IN THE EUCLIDEAN 3-DIMENSIONAL SPACE
Hardy spaces on the Euclidean space
Higher order rectifiability in Euclidean space
SIMILARITY PROPERTIES WHICH CHARACTERIZE EUCLIDEAN SPACE
Simple factor dressing and the López–Ros deformation of minimal surfaces in Euclidean 3-space
Holographic calculations of Euclidean Wilson loop correlator in Euclidean anti-de Sitter space
Geometric probabilities in the Euclidean space E3
Normal curves in n-dimensional Euclidean space
Some hemivariational inequalities in the Euclidean space
Framed slant helices in Euclidean 3-space
Solutions of the Generalized Weierstrass Representation in Four-Dimensional Euclidean Space
A new extragradient method for generalized variational inequality in Euclidean space
THE POLAR GEODESIC COORDINATE SYSTEM ON SURFACES IN THE EUCLIDEAN 3-DIMENSIONAL SPACE
Hardy spaces on the Euclidean space
Higher order rectifiability in Euclidean space
SIMILARITY PROPERTIES WHICH CHARACTERIZE EUCLIDEAN SPACE
Simple factor dressing and the López–Ros deformation of minimal surfaces in Euclidean 3-space
Holographic calculations of Euclidean Wilson loop correlator in Euclidean anti-de Sitter space
Geometric probabilities in the Euclidean space E3
Normal curves in n-dimensional Euclidean space
Some hemivariational inequalities in the Euclidean space