On a Class of Linear Weingarten Surfaces
作者: Vladimir I. PulovMariana Ts. HadzhilazovaIvaïlo 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.
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  • 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