On the Hamiltonian Minimality of Normal Bundles

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)


A Hamiltonian minimal (shortly, H-minimal) Lagrangian submanifold in a Kähler manifold is a critical point of the volume functional under all compactly supported Hamiltonian deformations. We show that any normal bundle of a principal orbit of the adjoint representation of a compact simple Lie group G in the Lie algebra \(\mathfrak{g}\) of G is an H-minimal Lagrangian submanifold in the tangent bundle \(T\mathfrak{g}\) which is naturally regarded as \(\mathbb{C}^{m}\). Moreover, we specify these orbits with this property in the class of full irreducible isoparametric submanifolds in the Euclidean space.


Symmetric Space Normal Bundle Lagrangian Submanifold Isoparametric Hypersurface Principal Orbit 
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The author would like to express his sincere thanks to Profs. Young Jin Suh, Jürgen Berndt, Yoshihiro Ohnita and Byung Hak Kim for inviting me to “Conference on real and complex submanifolds”. He was partially supported by Grant-in-Aid for JSPS Fellows.


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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Mathematical Institute, Graduate School of SciencesTohoku UniversityAoba-ku, SendaiJapan

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