Proceedings of the Japan Academy, Series A, Mathematical Sciences

Integral geometry and Hamiltonian volume minimizing property of a totally geodesic Lagrangian torus in $S^2 \times S^2$

Hiroshi Iriyeh, Hajime Ono, and Takashi Sakai

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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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 79, Number 10 (2003), 167-170.

Dates
First available in Project Euclid: 18 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1116443827

Digital Object Identifier
doi:10.3792/pjaa.79.167

Mathematical Reviews number (MathSciNet)
MR2028342

Zentralblatt MATH identifier
1055.53063

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C65: Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]

Keywords
Lagrangian submanifold Poincaré formula Hamiltonian stability

Citation

Iriyeh, Hiroshi; Ono, Hajime; Sakai, Takashi. 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 (2003), no. 10, 167--170. doi:10.3792/pjaa.79.167. https://projecteuclid.org/euclid.pja/1116443827


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