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.
- Standort
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Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
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Online-Ressource
- Sprache
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Englisch
- Erschienen in
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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)
- Urheber
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Dias, Diogo G.
Corro, Armando M. V.
- DOI
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10.1515/advgeom-2015-0040
- URN
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urn:nbn:de:101:1-2024022213291329444943
- Rechteinformation
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
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14.08.2025, 10:46 MESZ
Datenpartner
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Beteiligte
- Dias, Diogo G.
- Corro, Armando M. V.
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