TY - JOUR
T1 - Hamiltonian minimality of normal bundles over the isoparametric submanifolds
AU - Kajigaya, Toru
N1 - Funding Information:
A part of this work has been done while the author was staying at the King's College London by the “Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation by JSPS”. He expresses his sincere thanks to the hospitality of the college. He is grateful to Jürgen Berndt, Reiko Miyaoka and Gudlaugur Thorbergsson for valuable discussion and helpful comments. The author was partially supported by Grant-in-Aid for JSPS Fellows ( 12J04238 ).
Publisher Copyright:
© 2014 Published by Elsevier B.V.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - Let N be a complex flag manifold of a compact semi-simple Lie group G, which is standardly embedded in the Lie algebra g of G as a principal orbit of the adjoint action. We show that the normal bundle of N in g is a Hamiltonian minimal Lagrangian submanifold in the tangent space Tg which is naturally regarded as the complex Euclidean space. Moreover, we specify the complex flag manifolds with this property in the class of full irreducible isoparametric submanifolds in the Euclidean space.
AB - Let N be a complex flag manifold of a compact semi-simple Lie group G, which is standardly embedded in the Lie algebra g of G as a principal orbit of the adjoint action. We show that the normal bundle of N in g is a Hamiltonian minimal Lagrangian submanifold in the tangent space Tg which is naturally regarded as the complex Euclidean space. Moreover, we specify the complex flag manifolds with this property in the class of full irreducible isoparametric submanifolds in the Euclidean space.
KW - Complex flag manifolds
KW - Hamiltonian minimal Lagrangian submanifolds
KW - Isoparametric submanifolds
KW - Normal bundles
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U2 - 10.1016/j.difgeo.2014.09.004
DO - 10.1016/j.difgeo.2014.09.004
M3 - Article
AN - SCOPUS:84908576871
VL - 37
SP - 89
EP - 108
JO - Differential Geometry and its Applications
JF - Differential Geometry and its Applications
SN - 0926-2245
ER -