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On a theorem by do Carmo and Dajczer
Author(s):
Guido
Haak
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1547-1548.
MSC (1991):
Primary 53A10
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Abstract:
We give a new proof of a theorem by M.P. do Carmo and M. Dajczer on helicoidal surfaces of constant mean curvature.
References:
- 1.
- A. BOBENKO, All constant mean curvature tori in
, , in terms of theta-functions, Math. Ann., 290 (1991), pp. 209-245. MR 92h:53072 - 2.
- E. BOUR, Memoire sur le deformation de surfaces, Journal de l'Ecole Polytechnique, XXXIX Cahier (1862), pp. 1-148.
- 3.
- J. DORFMEISTER AND G. HAAK, On symmetries of constant mean curvature surfaces, preprint 197, KITCS and SFB288, 1996.
- 4.
- B. KONOPELCHENKO AND I. TAIMANOV, Constant mean curvature surfaces via an integrable dynamical system, J. Phys. A, 29 (1996), pp. 1261-1265. MR 97b:53015
- 5.
- M.P. DO CARMO AND M. DAJCZER, Helicoidal surfaces with constant mean curvature, Tohoku Math. Journal, 34 (1982), pp. 425-435. MR 84f:53003
- 6.
- U. PINKALL AND I. STERLING, On the classification of constant mean curvature tori, Annals of Math., 130 (1989), pp. 407-451. MR 91b:53009
- 7.
- T. SASAI, On helicoidal surfaces with constant mean curvature, Tokyo J. Math., 19 (1996), pp. 39-50. MR 97c:53015
- 8.
- B. SMYTH, A generalization of a theorem of Delaunay on constant mean curvature surfaces, in Statistical thermodynamics and differential geometry of microstructured materials, Springer, Berlin, Heidelberg, New York, 1993. MR 94f:53012
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Additional Information:
Guido
Haak
Affiliation:
Fachbereich Mathematik, TU-Berlin, D-10623 Berlin
Email:
haak@sfb288.math.tu-berlin.de
DOI:
10.1090/S0002-9939-98-04673-5
PII:
S 0002-9939(98)04673-5
Received by editor(s):
November 1, 1996
Additional Notes:
The author was supported by Sonderforschungsbereich 288.
Communicated by:
Christopher Croke
Copyright of article:
Copyright
1998,
American Mathematical Society
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