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Geometric Quantities of Manifolds with grassmann structure

Published online by Cambridge University Press:  11 January 2016

N. Bokan ,
P. Matzeu  and
Z. Rakić
N. Bokan
Affiliation:
Dipartimento di Matematica VialeMerello 92 09123Cagliari [email protected]
P. Matzeu
Affiliation:
Dipartimento di Matematica VialeMerello 92 09123Cagliari [email protected]
Z. Rakić
Affiliation:
Faculty of Mathematics University of Belgrade Studentski 16, PP 550 11001 BelgradeSerbia and [email protected]
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Abstract

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We study geometry of manifolds endowed with a Grassmann structure which depends on symmetries of their curvature. Due to this reason a complete decomposition of the space of curvature tensors over tensor product vector spaces into simple modules under the action of the group G = GL(p, ℝ) ⊗ GL(q, ℝ) is given. The dimensions of the simple submodules, the highest weights and some projections are determined. New torsion-free connections on Grassmann manifolds apart from previously known examples are given. We use algebraic results to reveal obstructions to the existence of corresponding connections compatible with some type of normalizations and to enlighten previously known results from another point of view.

Keywords

53C3022E45
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 180 , 2005 , pp. 45 - 76
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

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