Structures de Weyl admettant des spineurs parallèles
Compact lcK manifolds with parallel vector fields
We show that for n > 2 a compact locally conformally Kähler manifold (M2n , g, J) carrying a nontrivial parallel vector field is either Vaisman, or globally conformally Kähler, determined in an explicit way by a compact Kähler manifold of dimension 2n − 2 and a real function.
Kähler manifolds with small eigenvalues of the Dirac operator and a conjecture of Lichnerowicz
We describe all compact spin Kähler manifolds of even complex dimension and positive scalar curvature with least possible first eigenvalue of the Dirac operator.
Twistor forms on Kähler manifolds
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 forms in...
Special spinors and contact geometry.
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