Gadea, P. M.; Grifone, J.; Muñoz Masqué, J. Manifolds modelled over free modules over the double numbers. (English) Zbl 1049.58002 Acta Math. Hung. 100, No. 3, 187-203 (2003). 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. Reviewer: József Szilasi (Debrecen) Cited in 6 Documents MSC: 58A05 Differentiable manifolds, foundations 30G35 Functions of hypercomplex variables and generalized variables Keywords:B-analycity; B-holomorphy; manifolds over the double numbers; equidimensional supplementary foliations PDFBibTeX XMLCite \textit{P. M. Gadea} et al., Acta Math. Hung. 100, No. 3, 187--203 (2003; Zbl 1049.58002) Full Text: DOI