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

页码：1597 / 1603

页数：7

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