Abstract
By definition an orthogonal net on a pseudoriemannian manifold is a family of complementary foliations which intersect perpendicularly. There are derived generalizations of de Rham’s decomposition theorem by characterizing those pseudoriemannian manifolds equipped with an orthogonal net, which locally resp. globally allow a representation as a twisted resp. warped product. The results are applied for studying hypersurfaces with harmonic curvature.
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Meumertzheim, M., Reckziegel, H. & Schaaf, M. Decomposition of twisted and warped product nets. Results. Math. 36, 297–312 (1999). https://doi.org/10.1007/BF03322118
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DOI: https://doi.org/10.1007/BF03322118