Torsion-free H-structures in almost Abelian geometry

Speakers: Marco Freibert (Universität Hamburg)\n\nThe concept of an H-structure encompasses many important geometric structures on manifolds, including (almost) complex, (almost) symplectic, (almost) Hermitian and Kähler structures. Of particular interest are H-structures satisfying certain integrability conditions, such as torsion-freeness.\nIn this talk, we study invariant torsion-free H-structures on almost Abelian Lie groups G and associated compact quotients Γ\G. Such Lie groups are determined by a single endomorphism and, despite their simple algebraic description, provide many interesting examples and counterexamples in differential geometry, in particular in low dimensions.\nIn recent years, invariant geometric structures on almost Abelian Lie groups have been studied extensively, leading to characterisations and classifications of almost Abelian Lie groups admitting torsion-free H-structures in terms of their defining endomorphisms.\nI will present a general approach that unifies and substantially extends these results to broad classes of linear Lie groups H, revealing general conditions under which torsion-freeness implies flatness and yielding explicit characterisations also in many other cases.\n\nhttps://indico.math.cnrs.fr/event/17042/