Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(4): 1099-1108

Printed July 1, 2013

https://doi.org/10.4134/BKMS.2013.50.4.1099

Copyright © The Korean Mathematical Society.

Mannheim curves in 3-dimensional space forms

Jin Ho Choi, Tae Ho Kang, and Young Ho Kim

University of Ulsan, University of Ulsan, Kyungpook National University

Abstract

We define the Mannheim curve in a 3-dimensional Riemannian manifold, which is a generalization of the Mannheim curve in Euclidean space. In particular, we study the Mannheim curves and their partner curves in 3-dimensional space forms.

Keywords: Mannheim curves, Mannheim partner curves, space form

MSC numbers: Primary 53A04, 53A35