Abstract
Let M be a Riemannian manifold, ω a differentiable form on M with values in a bundle Hom (TM, ζ), and let G be an open subset of M such that Kerω forms a vector bundle ξ of constant fibre dimension k>0 over G. We prove: If ω satisfies some analytical conditions, then ξ is completely integrable, the integral manifolds of ξ are spherically bent in M, and in some interesting cases they are complete.
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Hiepko, S., Reckziegel, H. Über sphärische Blätterungen und die Vollständigkeit ihrer Blätter. Manuscripta Math 31, 269–283 (1980). https://doi.org/10.1007/BF01303277
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DOI: https://doi.org/10.1007/BF01303277