NAGATOMO Yasuyuki    Department   Undergraduate School  , School of Science and Technology    Position   Professor
Research Period	2005～2007
Research Topic	GLOBAL CONSTRUMONS OF MODULI SPACES
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.	17340018
Keyword	moduli spaces, harmonic mans, quaternion manifolds, twistor spaces, Lie groups, vector bundles, vanishing theorems, ASD connections
Responsibility	Representative Researcher
Representative Person	NAGATOMO Yasuyuki
Details	In 2007, we consider the cases that a harmonic map into Grassmannian is a totally geodesic one. As a result, we obtain the classification of totally geodesic immersions of irreducible type. In this classification, we obtain an integral formula which indicates the dimension of Grassmannian, which is the target space of the mapping. In the case of the complex projective line, we can show that an indecomposable totally geodesic immersion is an totally geodesic immersion of the irreducible type. To obtain the result, we use the above characterization of a harmonic map and construct a variant of the spherical function theory on homogeneous vector bundles. This implies that we can classify all totally geodesic immersions of complex projective line into Grassmannians. We develop an analogue of the "geometry of the twistor sections" on symmetric spaces of compact type. This gives us pairs of totally geodesic submanifolds on almost symmetric spaces of compact type. These pairs are intimately related to vector bundles and sections of them. Indeed, we can construct a function using a section, which is an isoparametric function on every Grassmann manifold. This function gives a family of submanifolds as level sets. We can find one and only minimal submanifold in this family.