Geometric Quantities of Manifolds with grassmann structure
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)...
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| Veröffentlicht in: | Nagoya mathematical journal 2005, Vol.180, p.45-76 |
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| container_title | Nagoya mathematical journal |
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| creator | Bokan, N. Matzeu, P. Rakić, Z. |
| description | 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. |
| doi_str_mv | 10.1017/S0027763000009181 |
| format | Article |
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| ispartof | Nagoya mathematical journal, 2005, Vol.180, p.45-76 |
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| source | Project Euclid Open Access; Freely Accessible Japanese Titles; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | 22E45 53C30 action of a group Grassmann manifold holonomy group irreducible representation normalization torsion-free connection |
| title | Geometric Quantities of Manifolds with grassmann structure |
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