We show that almost complex manifolds (M^4,J) of real dimension 4 for which the image of the Nijenhuis tensor forms a non-integrable bundle, called torsion bundle, admit a Z_2-structure locally, that is, a double absolute parallelism. In this way, the problem of equivalence for such almost complex manifolds can be solved; moreover, the classification of locally homogeneous manifold (M^4,J) is explicitly given when the Lie algebra of its infinitesimal automorphisms is non-solvable (indeed reductive). It is also shown that the group of the automorphisms of (M^4,J) is a Lie group of dimension less than or equal to 4, whose isotropy subgroup has at most two elements, and that there are not non-constant holomorphic functions on (M^4,J).

Almost complex manifolds with non-degenerate torsion / Bozzetti, Cristina; Medori, Costantino. - In: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS. - ISSN 0219-8878. - 14:3(2017), p. 1750033. [10.1142/S0219887817500335]

Almost complex manifolds with non-degenerate torsion

MEDORI, Costantino
2017

Abstract

We show that almost complex manifolds (M^4,J) of real dimension 4 for which the image of the Nijenhuis tensor forms a non-integrable bundle, called torsion bundle, admit a Z_2-structure locally, that is, a double absolute parallelism. In this way, the problem of equivalence for such almost complex manifolds can be solved; moreover, the classification of locally homogeneous manifold (M^4,J) is explicitly given when the Lie algebra of its infinitesimal automorphisms is non-solvable (indeed reductive). It is also shown that the group of the automorphisms of (M^4,J) is a Lie group of dimension less than or equal to 4, whose isotropy subgroup has at most two elements, and that there are not non-constant holomorphic functions on (M^4,J).
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2823734
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