Journal of Lie Theory 26 (2016), No. 4, 911--926
Copyright Heldermann Verlag 2016
An 1-Differentiable Cohomology Induced by a Vector Field
Mircea Crasmareanu
Faculty of Mathematics, University "Al. I. Cuza", Bd. Carol I no. 11, Iasi 700506, Romania
mcrasm@uaic.ro
Cristian Ida
Dept. of Mathematics and Computer Science, University "Transilvania", Bd. Iuliu Maniu no. 50, Brassov 500091, Romania
cristian.ida@unitbv.ro
Paul Popescu
Dept. of Applied Mathematics, University of Craiova, Str. Al. Cuza No. 13, Craiova 200585, Romania
Using the Lie derivative of a vector field, we define a cohomology on spaces of pairs of differential forms (or 1-differentiable forms) in a manifold. We provide a link to the classical de Rham cohomology and to a 1-differentiable cohomology of Lichnerowicz type associated to an one-form. We discuss also the case of a complex manifold and a holomorphic vector field. Finally, an application to the harmonicity of 1-differentiable forms is studied in a particular case.
Keywords: 1-differentiable form, Lie derivative, vector field, cohomology, harmonic form.
MSC: 14F40, 57R99, 58A10, 58A12
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