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1
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A classification of the torsion tensors on almost contact manifolds with B-metric

100%
Manev M., Ivanova M.
Open Mathematics
|
2014
|
tom 12
|
nr 10
1416-1432
EN
The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.
2
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Invariant connections and invariant holomorphic bundles on homogeneous manifolds

100%
Biswas I., Teleman A.
Open Mathematics
|
2014
|
tom 12
|
nr 1
1-13
EN
Let X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when X has an α-invariant complex structure).
3
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Einstein-Weyl structures on lightlike hypersurfaces

100%
Atindogbe C., Bérard-Bergery L., Ogouyandjou C.
Open Mathematics
|
2013
|
tom 11
|
nr 10
1850-1862
EN
We study Weyl structures on lightlike hypersurfaces endowed with a conformal structure of certain type and specific screen distribution: the Weyl screen structures. We investigate various differential geometric properties of Einstein-Weyl screen structures on lightlike hypersurfaces and show that, for ambient Lorentzian space ℝ1n+2 and a totally umbilical screen foliation, there is a strong interplay with the induced (Riemannian) Weyl-structure on the leaves.
4
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Hyperholomorphic connections on coherent sheaves and stability

68%
Verbitsky M.
Open Mathematics
|
2011
|
tom 9
|
nr 3
535-557
EN
Let M be a hyperkähler manifold, and F a reflexive sheaf on M. Assume that F (away from its singularities) admits a connection ▿ with a curvature Θ which is invariant under the standard SU(2)-action on 2-forms. If Θ is square-integrable, such sheaf is called hyperholomorphic. Hyperholomorphic sheaves were studied at great length in [21]. Such sheaves are stable and their singular sets are hyperkähler subvarieties in M. In the present paper, we study sheaves admitting a connection with SU(2)-invariant curvature which is not necessary L 2-integrable. We show that such sheaves are polystable.
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