双曲空间中的双曲广义框架曲面
Hyperbolic generalized framed surfaces in hyperbolic 3-space
AI总结：
本文在双曲3空间中引入双曲广义框架曲面的概念，研究其性质及与其他曲面的关系，并探讨了环形曲面的特性。
摘要：
在双曲3空间中，我们扩展了双曲框架曲面和一参数族双曲框架曲线的概念，引入了双曲广义框架曲面并建立了其关系。我们为光滑曲面成为双曲广义框架基曲面提供了必要且充分的条件，随后分析了双曲广义框架基曲面的奇点。此外，探讨了双曲广义框架曲面、广义框架曲面和光锥框架曲面之间的关系。作为双曲广义框架曲面的应用，我们研究了环形曲面的性质。
英文摘要：
Generalizing both hyperbolic framed surfaces and one-parameter families of hyperbolic framed curves, we introduce the concept of hyperbolic generalized framed surfaces and establish their relations in hyperbolic 3-space. We provide the necessary and sufficient conditions for a smooth surface to be a hyperbolic generalized framed base surface, followed by an analysis of the singularities of hyperbolic generalized framed base surfaces. Additionally, relations between hyperbolic generalized framed surfaces, generalized framed surfaces and lightcone framed surfaces are explored. As an application of hyperbolic generalized framed surfaces, we investigate the properties of horocyclic surfaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
