Harvey that the maximal order of an orientation preserving Periodic map on an orientable closed surface of genus g. g ≥ 2, is 4g+ 2. In this paper, we investigate the uniqueness of such maps. Harvey证明了在亏格为g,g≥2的可定向闭曲面上,保定向周期自同胚的最大阶是4g+2。
Integral absolute mean curvature is introduced to describe average curving of an orientable closed surface. 引入积分绝对平均曲率来描述可定向闭曲面的平均弯曲程度。
This paper studies the maximum genus of a graph$ G$ only in term of some embedding of$ G$ in an orientable surface, not of its other invariants, and gives the maximum genus of this kind of graphs. 不依赖图的其它参数,而主要依据图嵌入在定向曲面上的有关嵌入性质,该文研究图的最大亏格。
A graph is said to be upper embeddable if there exists a 2 cellular embedding on the orientable surface with one or two face. 若图G可2胞腔嵌入到可定向曲面S上,且G嵌入S后至多只有2个面,则称G在S上是上可嵌入的。
The orientable surface is named Seifert surface and the genus of knots is defined the minimal genus of the Seifert surface. 其中可定向的曲面称为Seifert曲面,纽结或链环的亏格定义为Seifert曲面的最小亏格。
A map is said to be orientable if the supporting surface is orientable. Otherwise, said to be non-orientable. 如果曲面是可定向的,那么称这个地图是可定向的,否则,称做不可定向的。