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Seminários do IMPA

Geometria Diferencial

Commuting pairs of generalized structures, para-hyper-Hermitian geometry and Born geometry
Ruxandra Moraru

University of Waterloo
Quarta-feira, 4 de dezembro de 2019, 15:30
Sala 236.

Let $M$ be a smooth manifold with tangent bundle $T$ and cotangent bundle $T^*$. By a generalized structure on $M$, we mean an endomorphism of $T \oplus T^*$ that squares to $\pm Id_{T \oplus T^*}$. In this talk, we consider pairs of generalized structures on $M$ whose product is a generalized metric. An example of such commuting pairs is given by generalized Kahler structures. There are three other types of such commuting pairs: generalized para-Kahler, generalized chiral and generalized anti-Kahler structures. We discuss the integrability of these structures and explain how para-hyper-Hermitian and Born geometry fit into this generalized context.