NAGATOMO Yasuyuki    Department   Undergraduate School  , School of Science and Technology    Position   Professor
Research Period	2002～2003
Research Topic	Differential equations and theory of submanifolds
Research Type	KAKENHI Research
Consignor	Japan Society for the Promotion of Science
Research Program Type	Grant-in-Aid for Scientific Research (C)
KAKENHI Grant No.	14540090
Keyword	Gauss map, 4 dimensional Kahler manifold, exceptional holonomy, isoparametric hypersurface, total curvature, homogeneous hypersurface, constant mean curvature surface, Seiberg-Witten equation
Responsibility	Research Contributor
Representative Person	MIYAOKA Reiko
Details	Moreover, using the fact that the family of isoparametric hypersurfaces fill the ambient space, we get an interesting relation between 13-dimensional sphere and 7-dimensional sphere. Furthermore, using that these hypersurfaces are given as orbits of the exceptional group G_2, we can show that there exists a metric on S^7-CP^2 of which holonomy group is G_2. From this, a real open version of Calabi conjecture will be considered, i.e., when a compact Riemannian manifolds with positive Ricci curvature from which a certain part removed, admits a metric with G_2 holonomy? In this way, hypersurfaces obtained as G_2 orbits suggest us very important and interesting problems.