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On the characteristic connection of gwistor space

100%

Albuquerque R.

Open Mathematics

2013

tom 11

nr 1

149-160

We give a brief presentation of gwistor spaces, which is a new concept from G 2 geometry. Then we compute the characteristic torsion T c of the gwistor space of an oriented Riemannian 4-manifold with constant sectional curvature k and deduce the condition under which T c is ∇c-parallel; this allows for the classification of the G 2 structure with torsion and the characteristic holonomy according to known references. The case of an Einstein base manifold is envisaged.

Hyperholomorphic connections on coherent sheaves and stability

81%

Verbitsky M.

Open Mathematics

2011

tom 9

nr 3

535-557

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.

Ograniczanie wyników

2 Open Mathematics

1 Albuquerque R.

1 Verbitsky M.

1 2013

1 2011

Wyniki wyszukiwania

On the characteristic connection of gwistor space

Hyperholomorphic connections on coherent sheaves and stability