Open Access
Dec. 2003 Integral geometry and Hamiltonian volume minimizing property of a totally geodesic Lagrangian torus in $S^2 \times S^2$
Hiroshi Iriyeh, Hajime Ono, Takashi Sakai
Proc. Japan Acad. Ser. A Math. Sci. 79(10): 167-170 (Dec. 2003). DOI: 10.3792/pjaa.79.167

Abstract

We prove that the product of equators $S^1 \times S^1$ in $S^2 \times S^2$ is globally volume minimizing under Hamiltonian deformations.

Citation

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Hiroshi Iriyeh. Hajime Ono. Takashi Sakai. "Integral geometry and Hamiltonian volume minimizing property of a totally geodesic Lagrangian torus in $S^2 \times S^2$." Proc. Japan Acad. Ser. A Math. Sci. 79 (10) 167 - 170, Dec. 2003. https://doi.org/10.3792/pjaa.79.167

Information

Published: Dec. 2003
First available in Project Euclid: 18 May 2005

zbMATH: 1055.53063
MathSciNet: MR2028342
Digital Object Identifier: 10.3792/pjaa.79.167

Subjects:
Primary: 53C40
Secondary: 53C65

Keywords: Hamiltonian stability , Lagrangian submanifold , Poincaré formula

Rights: Copyright © 2003 The Japan Academy

Vol.79 • No. 10 • Dec. 2003
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