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Jet isomorphism for conformal geometry

Robin C. Graham (2007)

Archivum Mathematicum

Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension is obstructed is described. A jet isomorphism theorem for even dimensional conformal geometry is formulated using the inhomogeneous ambient metrics recently introduced by the author...

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 of quasi-constant holomorphic sectional curvatures

Georgi Ganchev, Vesselka Mihova (2008)

Open Mathematics

The Kähler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kähler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric angle, associated with the section. A curvature identity characterizing such manifolds is found. The biconformal group of transformations whose elements transform Kähler metrics into Kähler ones is introduced and biconformal tensor invariants are obtained....

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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