Surfaces with harmonic inverse

mean curvature in space forms

Author:
Atsushi Fujioka

Journal:
Proc. Amer. Math. Soc. **127** (1999), 3021-3025

MSC (1991):
Primary 53A10; Secondary 53A05

Published electronically:
April 23, 1999

MathSciNet review:
1600144

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[B1]**A. I. Bobenko,*Surfaces of constant mean curvature and integrable equations*, Uspekhi Mat. Nauk**46**(1991), no. 4(280), 3–42, 192 (Russian); English transl., Russian Math. Surveys**46**(1991), no. 4, 1–45. MR**1138951**, 10.1070/RM1991v046n04ABEH002826**[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]**A. Gervasio Colares and Katsuei Kenmotsu,*Isometric deformation of surfaces in 𝑅³ preserving the mean curvature function*, Pacific J. Math.**136**(1989), no. 1, 71–80. MR**971934****[F]**Atsushi Fujioka,*Harmonic maps and associated maps from simply connected Riemann surfaces into the 3-dimensional space forms*, Tohoku Math. J. (2)**47**(1995), no. 3, 431–439. MR**1344911**, 10.2748/tmj/1178225525**[L]**H. Blaine Lawson Jr.,*Complete minimal surfaces in 𝑆³*, Ann. of Math. (2)**92**(1970), 335–374. MR**0270280****[P]**Bennett Palmer,*Spacelike constant mean curvature surfaces in pseudo-Riemannian space forms*, Ann. Global Anal. Geom.**8**(1990), no. 3, 217–226. MR**1089235**, 10.1007/BF00127936

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
53A10,
53A05

Retrieve articles in all journals with MSC (1991): 53A10, 53A05

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:
https://doi.org/10.1090/S0002-9939-99-04837-6

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

Published electronically:
April 23, 1999

Communicated by:
Christopher Croke

Article copyright:
© Copyright 1999
American Mathematical Society