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Session S19 - Geometric and Analytic Aspects of General Relativity

Wednesday, July 21, 17:00 ~ 18:00 UTC-3

Integrable structures in 4-manifolds

Bernardo Araneda

Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Germany   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Inspired by recent progress on the geometrical understanding of T-duality in string theory, we apply techniques from generalized and (para-)complex geometry to the analysis of different kinds of integrable structures in 4-manifolds equipped with a metric of Lorentzian, Riemannian, or split signature, with emphasis on applications to general relativity and twistor theory. In particular, we classify all (possibly complex-valued) almost para-Hermitian structures, we analyse their integrability, and we describe related constructions such as Lie and Courant algebroids, twisted de Rham complexes, deformations of (para-)complex structures, and two- and three-dimensional twistor spaces.

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