Journal of Lie Theory

no. 4
An 1-Differentiable Cohomology Induced by a Vector Field
Journal of Lie Theory, Volume 26 (2016) no. 4, pp. 911-926
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.
DOI: 10.5802/jolt.918
Classification: 14F40, 57R99, 58A10, 58A12
Keywords: 1-differentiable form, Lie derivative, vector field, cohomology, harmonic form 
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     author = {M. Crasmareanu and C. Ida and P. Popescu},
     title = {An {1-Differentiable} {Cohomology} {Induced} by a {Vector} {Field}},
     journal = {Journal of Lie Theory},
     pages = {911--926},
     year = {2016},
     volume = {26},
     number = {4},
     doi = {10.5802/jolt.918},
     zbl = {1361.58001},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.918/}
}
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M. Crasmareanu; C. Ida; P. Popescu. An 1-Differentiable Cohomology Induced by a Vector Field. Journal of Lie Theory, Volume 26 (2016) no. 4, pp. 911-926. doi: 10.5802/jolt.918

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