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Book Review
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Book Information
Author(s):
Udo Hertrich-Jeromin
Title:
Introduction to Möbius differential geometry
Additional book information:
London Mathematical Society Lecture Notes Series, vol. 300, Cambridge University Press,
Cambridge, UK,
2003,
xi+413,
US$50.00,
ISBN 0-521-53569-7
References:
-
- 1.
- M. A. Akivis and V. V. Goldberg, Conformal differential geometry and its generalizations, Wiley, New York, 1996. MR 1406793 (98a:53023)
- 2.
- W. Blaschke, Vorlesungen über Differentialgeometrie III: Differentialgeometrie der Kreise und Kugeln, Grundlehren XXIX, Springer, Berlin, 1929.
- 3.
- R. L. Bryant, A duality theorem for Willmore surfaces, J. Differential Geometry 20 (1984), 23-53. MR 0772125 (86j:58029)
- 4.
- T. E. Cecil, Lie sphere geometry, Springer, New York, 1992. MR 1219311 (94m:53076)
- 5.
- D. Ferus, K. Leschke, F. Pedit and U. Pinkall, Quaternionic holomorphic geometry: Plücker formula, Dirac eigenvalue estimates, and energy estimates of harmonic 2-tori, Invent. Math. 146 (2001), 507-593. MR 1869849 (2003a:53057)
- 6.
- G. Fubini, Applicabilità projettiva di due superficie, Palermo Rend. 41 (1916), 135-162.
- 7.
- U. Hertrich-Jeromin and U. Pinkall, Ein Beweis der Willmoreschen Vermutung für Kanaltori, J. Reine Angew. Math. 430 (1992), 21-34. MR 1172905 (95g:53067)
- 8.
- R. Kusner, Comparison surfaces for the Willmore problem, Pac. J. Math. 138 (1989), 317-345. MR 0996204 (90e:53013)
- 9.
- P. Li and S. T. Yau, A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces, Invent. Math 69 (1982), 269-291. MR 0674407 (84f:53049)
- 10.
- U. Pinkall, Dupin hypersurfaces, Math. Ann. 270 (1985), 427-440. MR 0774368 (86e:53044)
- 11.
- T. Takasu, Differentialgeometrien in den Kugelräumen, Bd. I, Tagaido Publ. Co., Kyoto, and Hafner Publ. Co., New York, 1938.
- 12.
- G. Thomsen, Über konforme Geometrie I: Grundlagen der konformen Flächentheorie, Hamb. Math. Abh. 3 (1923), 31-56.
- 13.
- J. H. White, A global invariant of conformal mappings in space, Proc. Amer. Math. Soc. 38 (1973), 162-164. MR 0324603 (48:2954)
- 14.
- T. J. Willmore, Note on embedded surfaces, An. Sti. Univ. Al. I. Cuza Iasi, N. Ser., Sect. Ia Mat. 11B (1965), 493-496. MR 0202066 (34:1940)
- 15.
- -, Surfaces in conformal geometry, Ann. Global Anal. Geom 18 (2000), 255-264. MR 1795097 (2001i:53099)
Additional Information:
Reviewer(s):
Thomas
E.
Cecil
Affiliation:
College of the Holy Cross
Email:
cecil@mathcs.holycross.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
42
(2005),
549-554.
MSC
(2000):
Primary 53A30
PII:
S 0273-0979(05)01067-0
Posted:
July 1, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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