Lie sphere geometry: with applications to submanifolds
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2008
|
| Edition: | 2. ed. |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 208 S. Ill., graph. Darst. 235 mm x 155 mm |
| ISBN: | 9780387746555 0387746552 |
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MARC
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| 100 | 1 | |a Cecil, Thomas E. |d 1945- |e Verfasser |0 (DE-588)102959354X |4 aut | |
| 245 | 1 | 0 | |a Lie sphere geometry |b with applications to submanifolds |c Thomas E. Cecil |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Springer |c 2008 | |
| 300 | |a XII, 208 S. |b Ill., graph. Darst. |c 235 mm x 155 mm | ||
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| 650 | 4 | |a Géométrie différentielle | |
| 650 | 4 | |a Sous-variétés (Mathématiques) | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Submanifolds | |
| 650 | 0 | 7 | |a Lie-Geometrie |0 (DE-588)4167647-6 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text |
Contents
Preface
to the First Edition
.
vii
Preface to the Second Edition
. ix
1
Introduction
. 1
2
Lie Sphere Geometry
. 9
2.1
Preliminaries
. 9
2.2
Möbius
Geometry of Unoriented Spheres
. 11
2.3
Lie Geometry of Oriented Spheres
. 14
2.4
Geometry of Hyperspheres in S" and H"
. 16
2.5
Oriented Contact and Parabolic Pencils of Spheres
. 19
3
Lie Sphere Transformations
. 25
3.1
The Fundamental Theorem
. 25
3.2
Generation of the Lie Sphere Group by Inversions
. 30
3.3
Geometric Description of Inversions
. 34
3.4
Laguerre Geometry
. 37
3.5
Subgeometries of Lie Sphere Geometry
. 46
4
Legendre Submanifolds
. 51
4.1
Contact Structure on
Л2""1
. 51
4.2
Definition of Legendre Submanifolds
. 56
4.3
The Legendre Map
. 60
4.4
Curvature Spheres and Parallel Submanifolds
. 64
4.5
Lie Curvatures and Isoparametric Hypersurfaces
. 72
4.6
Lie
invariance
of Tautness
. 82
4.7
Isoparametric Hypersurfaces of FKM-type
. 95
4.8
Compact Proper
Dupin
Submanifolds
. 112
xii
Contents
5
Dupin
Submanifolds
. 125
5.1
Local Constructions
. 125
5.2
Reducible
Dupin
Submanifolds
. 127
5.3
Lie Sphere Geometric Criterion for Reducibility
. 141
5.4
Cyclides of
Dupin
. 148
5.5
Lie Frames
. 159
5.6
Covariant Differentiation
. 165
5.7
Dupin
Hypersurfaces in 4-Space
. 168
References
. 191
Index
. 201 |
| adam_txt |
Contents
Preface
to the First Edition
.
vii
Preface to the Second Edition
. ix
1
Introduction
. 1
2
Lie Sphere Geometry
. 9
2.1
Preliminaries
. 9
2.2
Möbius
Geometry of Unoriented Spheres
. 11
2.3
Lie Geometry of Oriented Spheres
. 14
2.4
Geometry of Hyperspheres in S" and H"
. 16
2.5
Oriented Contact and Parabolic Pencils of Spheres
. 19
3
Lie Sphere Transformations
. 25
3.1
The Fundamental Theorem
. 25
3.2
Generation of the Lie Sphere Group by Inversions
. 30
3.3
Geometric Description of Inversions
. 34
3.4
Laguerre Geometry
. 37
3.5
Subgeometries of Lie Sphere Geometry
. 46
4
Legendre Submanifolds
. 51
4.1
Contact Structure on
Л2""1
. 51
4.2
Definition of Legendre Submanifolds
. 56
4.3
The Legendre Map
. 60
4.4
Curvature Spheres and Parallel Submanifolds
. 64
4.5
Lie Curvatures and Isoparametric Hypersurfaces
. 72
4.6
Lie
invariance
of Tautness
. 82
4.7
Isoparametric Hypersurfaces of FKM-type
. 95
4.8
Compact Proper
Dupin
Submanifolds
. 112
xii
Contents
5
Dupin
Submanifolds
. 125
5.1
Local Constructions
. 125
5.2
Reducible
Dupin
Submanifolds
. 127
5.3
Lie Sphere Geometric Criterion for Reducibility
. 141
5.4
Cyclides of
Dupin
. 148
5.5
Lie Frames
. 159
5.6
Covariant Differentiation
. 165
5.7
Dupin
Hypersurfaces in 4-Space
. 168
References
. 191
Index
. 201 |
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| ctrlnum | (OCoLC)173498965 (DE-599)DNB985166681 |
| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV023018274 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:12:02Z |
| indexdate | 2024-07-20T09:27:38Z |
| institution | BVB |
| isbn | 9780387746555 0387746552 |
| language | English |
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| physical | XII, 208 S. Ill., graph. Darst. 235 mm x 155 mm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Cecil, Thomas E. 1945- Verfasser (DE-588)102959354X aut Lie sphere geometry with applications to submanifolds Thomas E. Cecil 2. ed. New York, NY Springer 2008 XII, 208 S. Ill., graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Universitext Géométrie différentielle Sous-variétés (Mathématiques) Geometry, Differential Submanifolds Lie-Geometrie (DE-588)4167647-6 gnd rswk-swf Lie-Geometrie (DE-588)4167647-6 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2990411&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016222399&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cecil, Thomas E. 1945- Lie sphere geometry with applications to submanifolds Géométrie différentielle Sous-variétés (Mathématiques) Geometry, Differential Submanifolds Lie-Geometrie (DE-588)4167647-6 gnd |
| subject_GND | (DE-588)4167647-6 |
| title | Lie sphere geometry with applications to submanifolds |
| title_auth | Lie sphere geometry with applications to submanifolds |
| title_exact_search | Lie sphere geometry with applications to submanifolds |
| title_exact_search_txtP | Lie sphere geometry with applications to submanifolds |
| title_full | Lie sphere geometry with applications to submanifolds Thomas E. Cecil |
| title_fullStr | Lie sphere geometry with applications to submanifolds Thomas E. Cecil |
| title_full_unstemmed | Lie sphere geometry with applications to submanifolds Thomas E. Cecil |
| title_short | Lie sphere geometry |
| title_sort | lie sphere geometry with applications to submanifolds |
| title_sub | with applications to submanifolds |
| topic | Géométrie différentielle Sous-variétés (Mathématiques) Geometry, Differential Submanifolds Lie-Geometrie (DE-588)4167647-6 gnd |
| topic_facet | Géométrie différentielle Sous-variétés (Mathématiques) Geometry, Differential Submanifolds Lie-Geometrie |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2990411&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016222399&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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