Journal of the Mathematical Society of Japan

Special Lagrangian submanifolds invariant under the isotropy action of symmetric spaces of rank two

Kaname HASHIMOTO and Katsuya MASHIMO

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Abstract

We study special Lagrangian submanifolds of the cotangent bundle $T^*S^n$ of the sphere in the tangent space of Riemannian symmetric space of rank two. We show that the special Lagrangian submanifolds correspond to the solution of a differential equation on $\mathbb{R}^2$ under the assumption that the submanifold is of cohomogeneity one. Our result is the generalization of the former work of Sakai and the first author [5]. We study the qualitative properties of the solution for the special Lagrangian submanifolds and give some examples.

Article information

Source
J. Math. Soc. Japan, Volume 68, Number 2 (2016), 839-862.

Dates
First available in Project Euclid: 15 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1460727384

Digital Object Identifier
doi:10.2969/jmsj/06820839

Mathematical Reviews number (MathSciNet)
MR3488149

Zentralblatt MATH identifier
1348.53060

Subjects
Primary: 53C38: Calibrations and calibrated geometries

Keywords
special Lagrangian submanifold Calabi–Yau manifold calibration minimal hypersurface cohomogeneity one action

Citation

HASHIMOTO, Kaname; MASHIMO, Katsuya. Special Lagrangian submanifolds invariant under the isotropy action of symmetric spaces of rank two. J. Math. Soc. Japan 68 (2016), no. 2, 839--862. doi:10.2969/jmsj/06820839. https://projecteuclid.org/euclid.jmsj/1460727384


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