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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

Cristian Ida
Dept. of Mathematics and Computer Science, University "Transilvania", Bd. Iuliu Maniu no. 50, Brassov 500091, Romania

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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