EUDML

Currently displaying 1 – 4 of 4

Order by Relevance | Title | Year of publication

The structure tensor and first order natural differential operators

Piotr Kobak — 1992

Archivum Mathematicum

The notion of a structure tensor of section of first order natural bundles with homogeneous standard fibre is introduced. Properties of the structure tensor operator are studied. The universal factorization property of the structure tensor operator is proved and used for classification of first order $*$ -natural differential operators $\underset{̲}{D} : \underset{̲}{T \times T} \to \underset{̲}{T}$ for $n \geq 3$ .

Natural liftings of vector fields to tangent bundles of bundles of $1$ -forms

Piotr Kobak — 1991

Mathematica Bohemica

Natural liftings $D : I \to I T T^{*}$ are classified for $n \geq 2$ . It is proved that they form a 5-parameter family of operators.

The hyperKähler geometry associated to Wolf spaces

Piotr Kobak; Andrew Swann — 2001

Bollettino dell'Unione Matematica Italiana

Sia $G$ un grupo di Lie compatto e semplice. Sia $O_{min}$ la più piccola orbita nilpotente non-banale nell'algebra di Lie complessa $g^{C}$ . Si presenta una costruzione diretta di teoria di Lie delle metriche iperKahler su $O_{min}$ con potenziale Kahleriano $G$ -invariante e compatibili con la forma simplettica complessa di Kostant-Kirillov-Souriau. In particolare si ottengono le metriche iperKahler dei fibrati associati sugli spazi di Wolf (spazi simmetrici quaternionali a curvatura scalare positiva).