Category: ariel
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On the Dirac complement problem
Paper by T. Ariel, R. Rubio and M. Zambon. Abstract: The existence of a Dirac complement for a given Dirac structure is a central question in the structure theory of Courant algebroids and the deformation theory of Dirac structures. We study this problem in detail, proving the unobstructedness of lagrangian or local Dirac complements and…
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Obstructions to the existence of a Dirac complement
16 Sep 2025. Poster by Tom Ariel at the meeting of the Spanish Network of Geometry and Physics, Barcelona. Abstract: Dirac structures are a geometric object generalizing symplectic and Poisson structures. From a physics viewpoint, they describe mechanical systems with both symmetries and constraints. Geometrically, they are given by subbundles of a vector bundle with…
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Obstructions to the existence of a Dirac complement, poster
3 Jul 2025. Poster by Tom Ariel at the conference Interactions of Poisson Geometry, Lie Theory and Symmetry.
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The space of Dirac structures and the complement problem, by T. Ariel
Introduction to generalized metrics, Dirac structures and their integrability in terms of orthogonal transformations, the complement problem.