We show that almost complex manifolds (M4,J) of real dimension 4 for which the image of the Nijenhuis tensor forms a non-integrable bundle, called torsion bundle, admit a Z2-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 (M4,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 (M4,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 (M4,J).

Bozzetti, C., Medori, C. (2017). Almost complex manifolds with non-degenerate torsion. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 14(3) [10.1142/S0219887817500335].

Almost complex manifolds with non-degenerate torsion

BOZZETTI, CRISTINA;
2017

Abstract

We show that almost complex manifolds (M4,J) of real dimension 4 for which the image of the Nijenhuis tensor forms a non-integrable bundle, called torsion bundle, admit a Z2-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 (M4,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 (M4,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 (M4,J).
Articolo in rivista - Articolo scientifico
absolute parallelism; Almost complex manifold; non-degenerate torsion bundle;
Almost complex manifold, Absolute parallelism, Non-degenerate torsion bundle
English
Bozzetti, C., Medori, C. (2017). Almost complex manifolds with non-degenerate torsion. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 14(3) [10.1142/S0219887817500335].
Bozzetti, C; Medori, C
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/146860
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