{ "id": "1706.10068", "version": "v1", "published": "2017-06-30T08:49:47.000Z", "updated": "2017-06-30T08:49:47.000Z", "title": "Coverings for $4$-dimensional almost complex manifolds with non-degenerate torsion", "authors": [ "Cristina Bozzetti", "Costantino Medori" ], "comment": "17 pp", "categories": [ "math.DG", "math.CV" ], "abstract": "An almost complex manifolds $(M^4,J)$ of real dimension 4 with non-degenerate torsion bundle admit a double absolute parallelism and it is provided the classification of homogeneous $(M^4,J)$ having an associated non-solvable Lie algebra. We extend such a classification to the analysis of the manifolds having an associated solvable Lie algebra, up-to-coverings. Moreover, for homogeneous $(M^4,J)$ we provide examples with connected and non-connected double covering, thus proving that in general the double absolute parallelism is not the restriction of two absolute parallelisms. Furthermore, it is given the definition of a natural metric induced by the absolute parallelisms on $(M^4,J)$ and an example of an almost complex manifold with non-degenerate torsion endowed with that metric such that it becomes an almost K\\\"ahler manifold.", "revisions": [ { "version": "v1", "updated": "2017-06-30T08:49:47.000Z" } ], "analyses": { "keywords": [ "complex manifold", "double absolute parallelism", "non-degenerate torsion bundle admit", "dimensional", "associated non-solvable lie algebra" ], "note": { "typesetting": "TeX", "pages": 17, "language": "en", "license": "arXiv", "status": "editable" } } }