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三维空间型中闭曲面和测地球面的比较
引用本文:王幼宁.三维空间型中闭曲面和测地球面的比较[J].数学年刊A辑(中文版),2003(6).
作者姓名:王幼宁
作者单位:北京师范大学数学系 北京100875
基金项目:国家自然科学基金(No.19771010)资助的项目
摘    要:本文建立关于三维空间型中的可定向闭曲面的某些公式.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.在此意义上,可定向闭曲面可以与作为包含该闭曲面的凸的测地球的边界测地球面进行比较,这种比较能用于说明空间型自身的某些属性

关 键 词:可定向闭曲面  空间型  积分绝对平均曲率

COMPARISON BETWEEN CLOSED SURFACES AND GEODESIC SPHERES IN 3-DIMENSIONAL SPACE FORMS
WANG Youning.COMPARISON BETWEEN CLOSED SURFACES AND GEODESIC SPHERES IN 3-DIMENSIONAL SPACE FORMS[J].Chinese Annals of Mathematics,2003(6).
Authors:WANG Youning
Institution:WANG Youning Department of Mathematics,Beijing Normal University,Beijing 100875,China.
Abstract:This paper establishes some formulas on orientable closed surfaces in 3-dimensional space forms. Integral absolute mean curvature is introduced to describe average curving of an orientable closed surface. In this sense, an orientable closed surface could be compared with a geodesic sphere that is the boundary of a convex geodesic ball containing the orientable closed surface. The comparison can be used to show some properties of space forms only on themselves.
Keywords:Orientable closed surface  Space forms  Integral absolute mean curvature
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