Great circular surfaces in the three-sphere

In this paper, we consider a special class of the surfaces in the 3-sphere defined by one-parameter families of great circles. We give a generic classification of singularities of such surfaces and investigate the geometric meanings from the view point of spherical geometry.

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Bibliographic Details
Published in:	Differential geometry and its applications Vol. 29; no. 3; pp. 409 - 425
Main Authors:	Izumiya, Shyuichi, Nagai, Takayuki, Saji, Kentaro
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01-06-2011
Subjects:	Classification Differential geometry Extrinsic flat surface Great circle Great circles Great circular surface Singularities Spherical geometry The 3-sphere 58K40 The 3-sphere Great circle 57R45 Singularities Extrinsic flat surface 53A35 Spherical geometry Great circular surface
Online Access:	Get full text
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Summary:	In this paper, we consider a special class of the surfaces in the 3-sphere defined by one-parameter families of great circles. We give a generic classification of singularities of such surfaces and investigate the geometric meanings from the view point of spherical geometry.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0926-2245 1872-6984
DOI:	10.1016/j.difgeo.2011.02.005