A Differential Relation of Metric Properties for Orientable Smooth Surfaces in Double-struck capital R3

被引：2
|
作者：
Ryu, Sungmin [1 ]
机构：
[1] Incheon Natl Univ, Dept Mech Engn, Acad Ro 119, Incheon 22012, South Korea
来源：
MATHEMATICS | 2023年 / 11卷 / 10期
关键词：
orientable smooth surfaces; Gaussian curvature; angles of intersection;
D O I：
10.3390/math11102337
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Gauss-Bonnet formula finds applications in various fundamental fields. Global or local analysis on the basis of this formula is possible only in integral form since the Gauss-Bonnet formula depends on the choice of a simple region of an orientable smooth surface S. The objective of the present paper is to construct a differential relation of the metric properties concerned at a point on S. Pointwise analysis on S is possible through the differential relation, which is expected to provide new geometrical insights into existing studies where the Gauss-Bonnet formula is applied in integral form.
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页数：12
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