Poisson quasi-Nijenhuis manifolds and Dirac structures: A geometrical approach to deformation and involutive theorems

• Ano de defesa: 2024
• Autor(a) principal: Luiz, Murilo do Nascimento
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Courant algebroids; Dirac structures; Estuturas de Dirac; Poisson quasi-Nijenhuis manifolds; Quasi-Lie bialgebroides; Quasi-Lie bialgebroids; Twisting de um quase-Lie bialgebroid; Twists of quasi-Lie bialgebroids; Variedade de Poisson quasi-Nijenhuis
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-04062024-144344/

In this work, we analyze the connection between Poisson quasi-Nijenhuis structures, quasi-Lie bialgebroids, and Courant algebroids. We demonstrate how to deform a Poisson quasi-Nijenhuis manifold using a closed 2-form within the context of Courant algebroids and Dirac structures. Then, we interpret this procedure in the context of supermanifolds, as a specific instance of the so-called twisting of a proto-bialgebroid. Finally, we investigate the applications of Poisson quasi-Nijenhuis manifolds in the theory of integrable systems. The main results of this thesis are reported in (LUIZ; MENCATTINI; PEDRONI, 2024).