Geodesic
An 1-Differentiable Cohomology Induced by a Vector Field
Mircea Crasmareanu1 ; Cristian Ida2 ; Paul Popescu3, 4, 5, 6, 7
1Faculty of Mathematics, University "Al. I. Cuza", Bd. Carol I no. 11, Iasi 700506, Romania
2Dept. of Mathematics and Computer Science, University "Transilvania", Bd. Iuliu Maniu no. 50, Brassov 500091, Romania
3Dept. of Applied Mathematics, University of Craiova, Str. Al. Cuza No. 13, Craiova 200585, Romania
4Using 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.
5Keywords: 1-differentiable form, Lie derivative, vector field, cohomology, harmonic form.
6MSC: 14F40, 57R99, 58A10, 58A12
7[
Journal of Lie Theory, Tome 26 (2016) no. 4, pp. 911-926

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 14F40, 57R99, 58A10, 58A12
Mots-clés : 1-differentiable form, Lie derivative, vector field, cohomology, harmonic form

Mircea Crasmareanu  1   ; Cristian Ida  2   ; Paul Popescu  3 , 4 , 5 , 6 , 7

1 Faculty of Mathematics, University "Al. I. Cuza", Bd. Carol I no. 11, Iasi 700506, Romania
2 Dept. of Mathematics and Computer Science, University "Transilvania", Bd. Iuliu Maniu no. 50, Brassov 500091, Romania
3 Dept. of Applied Mathematics, University of Craiova, Str. Al. Cuza No. 13, Craiova 200585, Romania
4 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.
5 Keywords: 1-differentiable form, Lie derivative, vector field, cohomology, harmonic form.
6 MSC: 14F40, 57R99, 58A10, 58A12
7 [ 
Mircea Crasmareanu; Cristian Ida; Paul Popescu. An 1-Differentiable Cohomology Induced by a Vector Field. Journal of Lie Theory, Tome 26 (2016) no. 4, pp. 911-926. http://geodesic.mathdoc.fr/item/JOLT_2016_26_4_a0/
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     author = {Mircea Crasmareanu and Cristian Ida and Paul 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},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2016_26_4_a0/}
}
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