8 citations · 12 across the 4 of their papers we have counts for
5 papers
Chern's Conjecture in the Dupin case
Reiko Miyaoka
Chern's conjecture states that a closed minimal hypersurface in the euclidean sphere is isoparametric if it has constant scalar curvature. When the number of distinct principal…
Hamiltonian non-displaceability of Gauss images of isoparametric hypersurfaces
Hiroshi Iriyeh, Hui Ma, Reiko Miyaoka +1
In this article we study the Hamiltonian non-displaceability of Gauss images of isoparametric hypersurfaces in the spheres as Lagrangian submanifolds embedded in complex hyperquadr…
The Bryant-Salamon G_2 manifolds and hypersurface geometry
Reiko Miyaoka
We show that two of the Bryant-Salamon G_2-manifolds have a simple topology ; homeomorphic to the complement of some submanifolds of the 7-dimensional sphere. In this connection, w…
Dorfmeister-Neher's theorem on isoparametric hypersurfaces
Reiko Miyaoka
A new proof of the homogeneity of isoparametric hypersurfaces with six simple principal curvatures (Dorfmeister-Neher's theorem) is given in a method applicable to the multiplicity…
The Gauss map of pseudo-algebraic minimal surfaces
Y. Kawakami, R. Kobayashi, R. Miyaoka
We refine Osserman's argument on the exceptional values of the Gauss map of algebraic minimal surfaces. This gives an effective estimate for the number of exceptional values and th…