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Surfaces with harmonic inverse mean curvature in space forms
Author(s):
Atsushi
Fujioka
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3021-3025.
MSC (1991):
Primary 53A10;
Secondary 53A05
Posted:
April 23, 1999
MathSciNet review:
1600144
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Abstract:
We define surfaces with harmonic inverse mean curvature in space forms and generalize a theorem due to Lawson by which surfaces of constant mean curvature in one space form isometrically correspond to those in another. We also obtain an immersion formula, which gives a deformation family for these surfaces.
References:
- [B1]
- A. I. Bobenko, Constant mean curvature surfaces and integrable equations, Russian Math. Surveys 46:4 (1991), 1-45. MR 93b:53009
- [B2]
- A. I. Bobenko, Surfaces in terms of 2 by 2 matrices. Old and new integrable cases, Harmonic maps and Integrable Systems
 A.Fordy and J.C.Wood, eds. , Aspects of Mathematics, Vieweg, 1994, pp. 83-127. CMP 94:09 - [CK]
- G. Colares and K. Kenmotsu, Isometric deformation of surfaces in
 preserving the mean curvature function, Pacific J. Math. 136 (1989), 71-80. MR 89m:53011 - [F]
- A. Fujioka, Harmonic maps and associated maps from simply connected Riemann surfaces into the 3-dimensional space forms, T
 hoku Math. J. 47 (1995), 431-439. MR 96h:58045 - [L]
- B. Lawson, Complete minimal surfaces in
 , Ann. of Math. 92 (1970), 335-374. MR 42:5170 - [P]
- B. Palmer, Spacelike constant mean curvature surfaces in pseudo-Riemannian space forms, Ann. Global Anal. Geom. 8 (1990), 217-226. MR 91m:53051
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Additional Information:
Atsushi
Fujioka
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192 Japan
Address at time of publication:
Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192 Japan
Email:
fujioka@kappa.s.kanazawa-u.ac.jp
DOI:
10.1090/S0002-9939-99-04837-6
PII:
S 0002-9939(99)04837-6
Keywords:
Constant mean curvature surfaces,
surfaces with prescribed mean curvature
Received by editor(s):
March 20, 1997
Received by editor(s) in revised form:
December 4, 1997
Posted:
April 23, 1999
Communicated by:
Christopher Croke
Copyright of article:
Copyright
1999,
American Mathematical Society
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