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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).

The infinitesimal counterpart of tangent presymplectic groupoids of higher order

P. M. Kouotchop Wamba, A. MBA (2018)

Archivum Mathematicum

Let G , ω be a presymplectic groupoid. In this paper we characterize the infinitesimal counter part of the tangent presymplectic groupoid of higher order, ( T r G , ω c ) where T r G is the tangent groupoid of higher order and ω c is the complete lift of higher order of presymplectic form ω .

The integrability of a field of endomorphisms

Gerard Thompson (2002)

Mathematica Bohemica

A Theorem is proved that gives intrinsic necessary and sufficient conditions for the integrability of a zero-deformable field of endomorphisms. The Theorem is proved by reducing to a special case in which the endomorphism field is nilpotent. Many arguments used in the derivation of similar results are simplified, principally by means of using quotient rather than subspace constructions.

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