Manifolds modelled over free modules over the double numbers
Let \(\mathbb B:=\{z=x+jy\mid x,y\in \mathbb R,\;j^2=1\}\) be the algebra of double numbers. The authors introduce and study the concept of \(\mathbb B\)-differentiability, \(\mathbb B\)-analyticity and \(\mathbb B\)-holomorphy of a map \(F:U\to \mathbb B\) where \(U\subset \mathbb B^n\) is an open set. Next they turn to \(\mathbb B\)-manifolds and derive an important criterion for a \(2n\)-dimensional non-integrable \(\mathbb B\)-manifold to be a \(\mathbb B\)-manifold.
equidimensional supplementary foliations
scientific article; zbMATH DE number 2098987