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Seminários do IMPA

Geometric Strutures on Manifolds

Geometric structures on semidirect products of Lie groups
Anna Abasheva

HSE (Moscow)
Quinta-feira, 13 de fevereiro de 2020, 17:00
Sala 232

Maybe the most interesting example of a semidirect product of Lie groups is the tangent bundle to a Lie group. One can ask the following question: suppose G is a Lie group with a biinvarint metric, does TG admit a biinvariant metric too? The answer to this question is negative, however, Ilka Agricola and Christina Fereira constructed a family of so called naturally reductive structures on it. From the viewpoint of the Ambrose-Singer theorem which characterizes Riemannian homogeneous spaces among other Riemannian manifolds, naturally reductive structure is a generalization of biinvariant metric to homogeneous spaces. We shall discuss the construction and see how it generalizes to total spaces of tangent bundles to naturally reductive spaces. We shall also see that these spaces as well as their compact analogues admit a family of nearly Kähler structures.