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k -Dirac operator and the Cartan-Kähler theorem

Tomáš Salač (2013)

Archivum Mathematicum

We apply the Cartan-Kähler theorem for the k-Dirac operator studied in Clifford analysis and to the parabolic version of this operator. We show that for k = 2 the tableaux of the first prolongations of these two operators are involutive. This gives us a new characterization of the set of initial conditions for the 2-Dirac operator.

Kähler manifolds with split tangent bundle

Marco Brunella, Jorge Vitório Pereira, Frédéric Touzet (2006)

Bulletin de la Société Mathématique de France

This paper is concerned with compact Kähler manifolds whose tangent bundle splits as a sum of subbundles. In particular, it is shown that if the tangent bundle is a sum of line bundles, then the manifold is uniformised by a product of curves. The methods are taken from the theory of foliations of (co)dimension 1.

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