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Hamiltonian stationary normal bundles of surfaces in $\mathbf R^3$

Author(s): Makoto Sakaki
Journal: Proc. Amer. Math. Soc. 127 (1999), 1509-1515.
MSC (1991): Primary 53C42; Secondary 53A05
Posted: January 29, 1999
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Abstract: A surface in $\mathbf R^3$ has Hamiltonian stationary normal bundle if and only if it is either minimal, a part of a round sphere, or a part of a cone with vertex angle $\pi/2$ .

References:

1.: R. Harvey and H. B. Lawson, Calibrated geometries, Acta Math. 148 (1982), 47-157. MR 85i:53058
2.: Y.-G. Oh, Volume minimization of Lagrangian submanifolds under Hamiltonian deformations, Math. Z. 212 (1993), 175-192. MR 94a:58040

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Additional Information:

Makoto Sakaki
Affiliation: Department of Mathematics, Faculty of Science, Hirosaki University, Hirosaki 036, Japan
Address at time of publication: Department of Mathematical System Science, Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan
Email: sakaki@cc.hirosaki-u.ac.jp

DOI: 10.1090/S0002-9939-99-04700-0
PII: S 0002-9939(99)04700-0
Received by editor(s): June 16, 1997
Received by editor(s) in revised form: August 19, 1997
Posted: January 29, 1999
Dedicated: Dedicated to Professor Shukichi Tanno on his \emph{60}th birthday
Communicated by: Peter Li
Copyright of article: Copyright 1999, American Mathematical Society


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