Mathematics – Differential Geometry
Scientific paper
2011-05-16
Mathematics
Differential Geometry
16 pages
Scientific paper
We prove that the natural principal parameters on a given Weingarten surface are also natural principal parameters for the parallel surfaces of the given one. As a consequence of this result we obtain that the natural PDE of any Weingarten surface is the natural PDE of its parallel surfaces. We show that the linear fractional Weingarten surfaces are exactly the surfaces satisfying a linear relation between their three curvatures. Our main result is classification of the natural PDE's of Weingarten surfaces with linear relation between their curvatures.
Ganchev Georgi
Mihova Vesselka
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