Book Review
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Book Information:
Author: 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 pp., ISBN 0-521-53569-7, US$50.00
- 1. Maks A. Akivis and Vladislav V. Goldberg, Conformal differential geometry and its generalizations, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1996. A Wiley-Interscience Publication. MR 1406793
- 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. Thomas E. Cecil, Lie sphere geometry, Universitext, Springer-Verlag, New York, 1992. With applications to submanifolds. MR 1219311
- 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), no. 3, 507–593. MR 1869849, https://doi.org/10.1007/s002220100173
- 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 (German). MR 1172905, https://doi.org/10.1515/crll.1992.430.21
- 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. James H. White, A global invariant of conformal mappings in space, Proc. Amer. Math. Soc. 38 (1973), 162–164. MR 0324603, https://doi.org/10.1090/S0002-9939-1973-0324603-1
- 14. T. J. Willmore, Note on embedded surfaces, An. Şti. Univ. “Al. I. Cuza” Iaşi Secţ. I a Mat. (N.S.) 11B (1965), 493–496 (English, with Romanian and Russian summaries). MR 0202066
- 15. T. J. Willmore, Surfaces in conformal geometry, Ann. Global Anal. Geom. 18 (2000), no. 3-4, 255–264. Special issue in memory of Alfred Gray (1939–1998). MR 1795097, https://doi.org/10.1023/A:1006717506186
Review Information:
Reviewer: Thomas E. Cecil
Affiliation: College of the Holy Cross
Email: cecil@mathcs.holycross.edu
Journal: Bull. Amer. Math. Soc. 42 (2005), 549-554
MSC (2000): Primary 53A30
Published electronically: July 1, 2005
Review copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
