
Journal of Lie Theory 26 (2016), No. 4, 911926 Copyright Heldermann Verlag 2016 An 1Differentiable 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 1differentiable forms) in a manifold. We provide a link to the classical de Rham cohomology and to a 1differentiable cohomology of Lichnerowicz type associated to an oneform. We discuss also the case of a complex manifold and a holomorphic vector field. Finally, an application to the harmonicity of 1differentiable forms is studied in a particular case. Keywords: 1differentiable form, Lie derivative, vector field, cohomology, harmonic form. MSC: 14F40, 57R99, 58A10, 58A12 [ Fulltextpdf (287 KB)] for subscribers only. 