Geodesic
Integration of vector fields on smooth and holomorphic supermanifolds
Documenta mathematica, Tome 18 (2013), pp. 519-545
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We give a new and self-contained proof of the existence and unicity of the flow for an arbitrary (not necessarily homogeneous) smooth vector field on a real supermanifold, and extend these results to the case of holomorphic vector fields on complex supermanifolds. Furthermore we discuss local actions associated to super vector fields, and give several examples and applications, as, e.g., the construction of an exponential morphism for an arbitrary finite-dimensional Lie supergroup.
DOI : 10.4171/dm/408
Classification : 32C11, 37C10, 57S20, 58A50
Mots-clés : group actions, vector fields, supermanifolds, flows 
@article{10_4171_dm_408,
     author = {St\'ephane Garnier and Tilmann Wurzbacher},
     title = {Integration of vector fields on smooth and holomorphic supermanifolds},
     journal = {Documenta mathematica},
     pages = {519--545},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/408},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/408/}
}
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Stéphane Garnier; Tilmann Wurzbacher. Integration of vector fields on smooth and holomorphic supermanifolds. Documenta mathematica, Tome 18 (2013), pp. 519-545. doi: 10.4171/dm/408

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