General Mathematics, Vol. 5, No. 1 - 4, pp. 347-370, 1995

H. Reckziegel and M. Schaaf -- Decomposition Theorems in Differential Geometry

Abstract: By definition a net on a manifold is a family of complementary foliations. Nets and net morphisms between netted manifolds allow to develop basic tools for the decomposability of netted manifolds. In this way new generalizations of de Rham's decomposition theorem are obtained. In a second part the decomposability of isometric immersions from a warped product into a pseudoriemannian manifold equipped with a warped product net is investigated. In particular N\"olkers classification of warped product representations of the standard spaces of constant curvature and his generalization of Moore's decomposition theorem of isometric immersions \,$M_1\times\cdots\times M_k \to \R^n$\, are described.

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