Seiichi Udagawa

Harmonic tori in quaternionic projective 3-spaces

Burstall classified conformal non-superminimal harmonic two-tori in spheres and complex projective spaces. In this paper, we shall classify conformal non-superminimal harmonic two-tori in a 2or 3-dimensional quaternionic protective space, which are not always covered by primitive harmonic two-tori of finite type.

CHARACTERIZATIONS OF RICCI FLAT METRICS AND LAGRANGIAN SUBMANIFOLDS IN TERMS OF THE VARIATIONAL PROBLEM

Given the pair ( P , η) of (0,2) tensors, where η defines a volume element, we consider a new variational problem varying η only. We then have Einstein metrics and slant immersions as critical points of the 1st variation. We may characterize Ricci flat metrics and Lagrangian submanifolds as stable critical points of our variational problem.

Characterization of Parallel Isometric Immersions of Space Forms into Space Forms in the Class of Isotropic Immersions

For an isotropic submanifold M n (n ≧ 3) of a space form e M n+p (c) of constant sectional curvature c, we show that if the mean curvature vector of M n is parallel and the sectional curvature K of M n satisfies some inequality, then the second fundamental form of M n in e M n+p is parallel and our