## Integration of vector fields on smooth and holomorphic supermanifolds

### Summary

Summary: 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.

### Mathematics Subject Classification

58A50, 37C10, 57S20, 32C11

### Keywords/Phrases

supermanifolds, vector fields, flows, group actions