Tohoku Mathematical Journal

Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces

Amartuvshin Amarzaya and Yoshihiro Ohnita

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Abstract

A compact minimal Lagrangian submanifold immersed in a Kähler manifold is called Hamiltonian stable if the second variation of its volume is nonnegative under all Hamiltonian deformations. We study compact Hamiltonian stable minimal Lagrangian submanifolds with parallel second fundamental form embedded in complex projective spaces. Moreover, we completely determine Hamiltonian stability of all real forms in compact irreducible Hermitian symmetric spaces, which were classified previously by M. Takeuchi.

Article information

Source
Tohoku Math. J. (2), Volume 55, Number 4 (2003), 583-610.

Dates
First available in Project Euclid: 11 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1113247132

Digital Object Identifier
doi:10.2748/tmj/1113247132

Mathematical Reviews number (MathSciNet)
MR2017227

Zentralblatt MATH identifier
1062.53053

Subjects
Primary: 53Cxx: Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx]
Secondary: 53Dxx: Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]

Keywords
Lagrangian submanifold minimal submanifold Hamiltonian stability symplectic geometry

Citation

Amarzaya, Amartuvshin; Ohnita, Yoshihiro. Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces. Tohoku Math. J. (2) 55 (2003), no. 4, 583--610. doi:10.2748/tmj/1113247132. https://projecteuclid.org/euclid.tmj/1113247132


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References

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