Dupin Submanifolds in Lie Sphere Geometry

Springer Collected Works in Mathematics - Selected Papers IV ◽

10.1007/978-1-4614-9451-5_19 ◽

1989 ◽

pp. 269-330

Author(s):

Shiing-Shen Chern

Keyword(s):

Lie Sphere Geometry ◽

Sphere Geometry ◽

Lie Sphere

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Homogeneous surfaces in Lie sphere geometry

Geometriae Dedicata ◽

10.1007/s10711-010-9460-4 ◽

2010 ◽

Vol 149 (1) ◽

pp. 15-43 ◽

Cited By ~ 1

Author(s):

Tongzhu Li

Keyword(s):

Lie Sphere Geometry ◽

Sphere Geometry ◽

Lie Sphere

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Dupin Hypersurfaces in Lie Sphere Geometry

Geometry and Analysis on Manifolds - Progress in Mathematics ◽

10.1007/978-3-319-11523-8_15 ◽

2015 ◽

pp. 383-394 ◽

Cited By ~ 3

Author(s):

Gary R. Jensen

Keyword(s):

Lie Sphere Geometry ◽

Sphere Geometry ◽

Dupin Hypersurfaces ◽

Lie Sphere

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Discrete channel surfaces

Mathematische Zeitschrift ◽

10.1007/s00209-019-02389-4 ◽

2019 ◽

Vol 294 (1-2) ◽

pp. 747-767

Author(s):

Udo Hertrich-Jeromin ◽

Wayne Rossman ◽

Gudrun Szewieczek

Keyword(s):

Discrete Version ◽

Smooth Channel ◽

Lie Sphere Geometry ◽

Discrete Channel ◽

Channel Surface ◽

Sphere Geometry ◽

Definition Of ◽

Lie Sphere

Abstract We present a definition of discrete channel surfaces in Lie sphere geometry, which reflects several properties for smooth channel surfaces. Various sets of data, defined at vertices, on edges or on faces, are associated with a discrete channel surface that may be used to reconstruct the underlying particular discrete Legendre map. As an application we investigate isothermic discrete channel surfaces and prove a discrete version of Vessiot’s Theorem.

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Classification of surfaces in three-sphere in Lie sphere geometry

Nagoya Mathematical Journal ◽

10.1017/s0027763000005924 ◽

1996 ◽

Vol 143 ◽

pp. 59-92

Author(s):

Takayoshi Yamazaki ◽

Atsuko Yamada Yoshikawa

Keyword(s):

Plane Curves ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Three Sphere ◽

Lie Sphere Geometry ◽

Sphere Geometry ◽

Necessary And Sufficient ◽

Lie Sphere

We studied plane curves in Lie sphere geometry in [YY]. Especially we constructed Lie frames of curves in S2 and classified them by the Lie equivalence. In this paper we are concerned with surfaces in S3. We construct Lie frames and classify them. We moreover obtain the necessary and sufficient condition that two surfaces are Lie equivalent.

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