| Autor: |
Dias, Diogo G., Corro, Armando M. V. |
| Předmět: |
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| Zdroj: |
Advances in Geometry; Jan2016, Vol. 16 Issue 1, p45-55, 11p |
| Abstrakt: |
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 linearWeingarten 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 aWeierstrass type representation (in short, EDSGWsurfaces). 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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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