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Displaying similar documents to “A Geometric Realization of s l ( 6 , ℂ ) ”

Lie Algebra bundles on s-Kähler manifolds, with applications to Abelian varieties

Giovanni Gaiffi, Michele Grassi (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove that one can obtain natural bundles of Lie algebras on rank two s -Kähler manifolds, whose fibres are isomorphic respectively to so ( s + 1 , s + 1 ) , su ( s + 1 , s + 1 ) and sl ( 2 s + 2 , ℝ ) . These bundles have natural flat connections, whose flat global sections generalize the Lefschetz operators of Kähler geometry and act naturally on cohomology. As a first application, we build an irreducible representation of a rational form of su ( s + 1 , s + 1 ) on (rational) Hodge classes of Abelian varieties with rational period matrix.

Twistor forms on Kähler manifolds

Andrei Moroianu, Uwe Semmelmann (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Twistor forms are a natural generalization of conformal vector fields on riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We study twistor forms on compact Kähler manifolds and give a complete description up to special forms in the middle dimension. In particular, we show that they are closely related to hamiltonian 2-forms. This provides the first examples of compact Kähler manifolds with non–parallel twistor...