On a Class of Linear Weingarten Surfaces

  title={On a Class of Linear Weingarten Surfaces},
  author={Vladimir Pulov and Mariana Ts. Hadzhilazova and Iva{\"i}lo M. Mladenov},
We consider a class of linear Weingarten surfaces of revolution whose principal curvatures, meridional kμ and parallel kπ , satisfy the relation kμ = (n + 1)kπ , n = 0, 1, 2, . . . . The first two members of this class of surfaces are the sphere (n = 0) and the Mylar balloon (n = 1). Elsewhere the Mylar balloon has been parameterized via the Jacobian and Weierstrassian elliptic functions and elliptic integrals. Here we derive six alternative parameterizations describing the third type of… 
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