An 1-differentiable cohomology induced by a vector field

2014/06/22 by Mircea Crasmareanu, Crasmareanu, Mircea, Cristian Ida +3 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1406.5714

arxiv created 2014/06/22 · arxiv updated 2014/06/24

Abstract

A new cohomology, induced by a vector field, is defined on pairs of differential forms (1--differentiable forms) in a manifold. It is proved a link with the classical de Rham cohomology and an 1-differentable cohomology of Lichnerowicz type associated to an one form. Also, the case when the manifold is complex and the vector field is holomorphic is studied. Finally, an application of this theory to the harmonicity of 1-differentiable forms is studied in a particular case.

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