NAGATOMO Yasuyuki    Department   Undergraduate School  , School of Science and Technology    Position   Professor
Research Period	2001～2003
Research Topic	Differential geometry of harmonic maps, minimal submanifolds and Yang-Mills-Higgs equations
Research Type	KAKENHI Research
Consignor	Japan Society for the Promotion of Science
Research Program Type	Grant-in-Aid for Scientific Research (B)
KAKENHI Grant No.	13440025
Keyword	Lagrange submanifold, harmonic map, moduli space, differential geometry, minimal submanifold, Yang-Mills-Higgs equation
Responsibility	Research Contributor
Representative Person	OHNITA Yoshihiro
Details	The joint work of Ohnita and Udagawa on harmonic maps of finite type was published in the proceedings of the 9-th MSJ-IRI. It is related with the equivalence problem among twisted loop algebras associated with different k-symmetric spaces and we will go to further research. And Ohnita discussed pluriharmonic maps into symmetric spaces from the viewpoint of integrable systems and proved DPW formula for pluriharmonic maps. In the joint work with James Eells on the structure of spaces of harmonic maps we started from the precise proof that the space of harmonic maps between compact real analytic Riemannian manifols is a real analytic space, and we are still working. From the viewpoint of a new area in minimal submanifold theory, Ohnita studies the Hamiltonian stability problem of Lagrangian submanifolds in K"ahler manifolds. By the Lie theoretic method, he showed that compact minimal irreducible symmetric Lagrangian submanifolds embedded in complex projective spaces are Hamiltonian stable. Moreover, we proved that compact symmetric Lagrangian submanifolds embedded in complex Euclidean spaces. And we discuss the relationship between Lagrangian submanifolds and the moment maps. Until now only known Hamiltonian stable Lagrangian submanifolds in complex projective spaces and complex Euclidean spaces. Were real projective subspaces and Clifford tori. However we gave many rich examples of Hamiltonian stable Lagrangian submanifolds in the class of Lagrangian submanifolds with parallel second fundamental form, namely symmetric Lagrangian submanifolds. Koike has succeeded in construction of theory for complex equifocal submanifolds in symmetri spaces and isoparametric submanifolds in Hilbert spaces in the case of noncompact type. It is an answer to a problem posed by Terng-Thorgergsson.