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Hiroshi Tamaru （Hiroshima Univ.） |
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| Title : |
Left-invariant metrics on Lie groups and submanifold geometry |
Abstract
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Left-invariant Riemannian metrics on Lie groups have provided
many interesting examples of homogeneous Einstein and Ricci soliton
manifolds. In general, it is not easy to examine whether a given Lie group
admit such distinguished metrics or not. In this talk, I will explain our
approach from submanifold geometry. In particular, for three-dimensional
solvable Lie groups, the existence and nonexistence of left-invariant Ricci
solitons have a nice correspondence with the geometry of cohomogeneity one
actions on some noncompact symmetric space. I will also mention some
higher-dimensional examples and a pseudo-Riemannian version.
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Organizer: Reiko Miyaoka
Contact：
Grants-in-Aids for Scientific research：23340012 |
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