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Classification of surfaces of Delaunay type. (Classification des surfaces de type Delaunay.) (French) Zbl 0972.53007

The authors define and study complete and noncomplete rotational \(f\)-special Weingarten surfaces in Euclidean space, where \(f\) is a function of class \(C^1\) on \([0;+ \infty[\) and \(h=f(H^2-K)\), \(H\) and \(K\) denote mean and Gauss curvature, respectively. Assuming some conditions on \(f\) the authors prove general existence and uniqueness theorems for such complete surfaces and classify \(f\)-special surfaces.

MSC:

53A05 Surfaces in Euclidean and related spaces
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