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Berndt Jurgen (King's College London) |
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| Title : Polar actions on symmetric spaces |
Abstract
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An isometric action of a connected Lie group on a Riemannian manifold
is called polar if there exists a connected closed submanifold which meets
each orbit of the action and intersects it orthogonally. Dadok established
in 1985 a remarkable, and mysterious, relation between polar actions on
Euclidean spaces and Riemannian symmetric spaces. Soon afterwards an attempt
was made to classify polar actions on symmetric spaces. For irreducible
symmetric spaces of compact type the final step of the classification has
just been completed by Kollross and Lytchak. In the talk I want to focus
on symmetric spaces of noncompact type. For actions of reductive groups
one can use the concept of duality between symmetric spaces of compact
type and of noncompact type. However, new examples and phenomena arise
from the geometry induced by actions of parabolic subgroups, for which
there is no analogon in the compact case. I plan to discuss the main difficulties
one encounters here and some partial solutions.
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Organizer: Reiko Miyaoka
Contact：
Grants-in-Aids for Scientific research：23340012 |
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