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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.

Kähler-Einstein metrics singular along a smooth divisor

Raffe Mazzeo (1999)

Journées équations aux dérivées partielles

In this note we discuss some recent and ongoing joint work with Thalia Jeffres concerning the existence of Kähler-Einstein metrics on compact Kähler manifolds which have a prescribed incomplete singularity along a smooth divisor D . We shall begin with a general discussion of the problem, and give a rough outline of the “classical” proof of existence in the smooth case, due to Yau and Aubin, where no singularities are prescribed. Following this is a discussion of the geometry of the conical or edge...

K-contact A-manifolds

WŁodzimierz Jelonek (1998)

Colloquium Mathematicae

The aim of this paper is to give a characterization of regular K-contact A-manifolds.

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