Splitting theorems in presence of an irrotational vector field

Details Splitting theorems in presence of an irrotational vector field Splitting theorems in presence of an irrotational vector field

2003-06-24

arxiv.org/abs/math/0306343v1

Mathematics

Differential Geometry

14 pages

Scientific paper

New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can get twisted, warped or direct decompositions. Some applications to Lorentzian manifold are shown and also $\mathbf{S}^{1}\times L$ type decomposition is treated.

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