On a theorem by do Carmo and Dajczer

Author:
Guido Haak

Journal:
Proc. Amer. Math. Soc. **126** (1998), 1547-1548

MSC (1991):
Primary 53A10

DOI:
https://doi.org/10.1090/S0002-9939-98-04673-5

MathSciNet review:
1476135

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Abstract | References | Similar Articles | Additional Information

Abstract: We give a new proof of a theorem by M.P. do Carmo and M. Dajczer on helicoidal surfaces of constant mean curvature.

**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:
https://doi.org/10.1090/S0002-9939-98-04673-5

Received by editor(s):
November 1, 1996

Additional Notes:
The author was supported by Sonderforschungsbereich 288.

Communicated by:
Christopher Croke

Article copyright:
© Copyright 1998
American Mathematical Society