A generalization of Lancret's theorem

被引：43
|
作者：
Ciftci, Uenver [1 ]
机构：
[1] Namk Kemal Univ, Fen Edebiyat Fak, TR-59100 Tekirdag, Turkey
来源：
JOURNAL OF GEOMETRY AND PHYSICS | 2009年 / 59卷 / 12期
关键词：
General helix; Lancret's theorem; Curves in Lie groups; LIE-GROUPS; N-SPACE; HELICES; HYPERSURFACES; CURVATURE; SURFACES; CURVES;
D O I：
10.1016/j.geomphys.2009.07.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
General helices in a three dimensional Lie group with a bi-invariant metric are defined and a generalization of Lancret's theorem is obtained. We conclude that the so-called spherical images of general helices are plane curves, and we obtain the so-called spherical general helices. We also give a relation between the geodesics of the so-called cylinders and general helices. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码：1597 / 1603
页数：7
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