On a Class of Linear Weingarten Surfaces
 作者： Vladimir I. Pulov ,  Mariana Ts. Hadzhilazova ,  Ivaïlo M. Mladenov 论文集英文名称： Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization 来源数据库： Project Euclid DOI： 10.7546/giq-19-2018-168-187 原始语种摘要： We consider a class of linear Weingarten surfaces of revolution whose principal curvatures, meridional $k_{\mu}$ and parallel $k_{\pi}$, satisfy the relation $k_{\mu}=(n+1)k_{\pi}$, $n=0,\,1,\,2,\ldots\, .$ 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 surfaces when $n=2$. The so obtained explicit formulas are applied for the derivation of the basic geometrical characteristics of this surface.

• elliptic　椭圆形的
• Jacobian　雅可比
• explicit　明白
• Mylar　聚酯薄膜
• consider　仔细考虑
• Class　B类放大器、 C类放大器
• satisfy　满足
• basic　基本的
• sphere
• balloon　气球