7 papers
Non-existence of exceptional orbits under polar actions on Hilbert spaces
Masahiro Morimoto
We prove that any polar action on a separable Hilbert space by a connected Hilbert Lie group does not have exceptional orbits. This generalizes a result of Berndt, Console and Olmo…
Path group actions induced by sigma-actions and affine Kac-Moody symmetric spaces of group type
Masahiro Morimoto
In 1995, C.-L. Terng associated to each hyperpolar action on a compact symmetric space, a hyperpolar proper Fredholm (PF) action on a Hilbert space. This is a group action by an in…
Curvatures and austere property of orbits of path group actions induced by Hermann actions
Masahiro Morimoto
It is known that an isometric action of a Lie group on a compact symmetric space gives rise to a proper Fredholm action of a path group on a path space via the gauge transformation…
On weakly reflective submanifolds in compact isotropy irreducible Riemannian homogeneous spaces
Masahiro Morimoto
We show that for any weakly reflective submanifold of a compact isotropy irreducible Riemannian homogeneous space its inverse image under the parallel transport map is an infinite…
Austere and arid properties for PF submanifolds in Hilbert spaces
Masahiro Morimoto
Austere submanifolds and arid submanifolds constitute respectively two different classes of minimal submanifolds in finite dimensional Riemannian manifolds. In this paper we introd…
On weakly reflective PF submanifolds in Hilbert spaces
Masahiro Morimoto
A weakly reflective submanifold is a minimal submanifold of a Riemannian manifold which has a certain symmetry at each point. In this paper we introduce this notion into a class of…