Boryczka, Grzegorz; Tovar, Luis Manuel Hyperbolic-like manifolds, geometrical properties and holomorphic mappings. (English) Zbl 0887.46006 Ławrynowicz, J. (ed.), Generalizations of complex analysis and their applications in physics. Warszawa: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 37, 53-66 (1996). Summary: The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudo-distance \(\rho^\alpha_X(z_0, z)[{\mathcal U}]\) introduced by P. Dolbeault and J. Ławrynowicz [Sel. Pap. Semin. Łodz/Poland 1985/87, 191-204 (1989; Zbl 0663.32018)] in connection with bordered holomorphic chains of dimension one. Several properties of the related hyperbolic-like manifolds are considered remarking the analogies with and differences from the familiar hyperbolic and Stein manifolds. Likewise several examples are treated in detail.For the entire collection see [Zbl 0856.00020]. MSC: 46C20 Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) 32H25 Picard-type theorems and generalizations for several complex variables 32G81 Applications of deformations of analytic structures to the sciences Keywords:Dirichlet integral-type biholomorphic-invariant pseudo-distance; bordered holomorphic chains; hyperbolic-like manifolds; Stein manifolds Citations:Zbl 0663.32018 PDFBibTeX XMLCite \textit{G. Boryczka} and \textit{L. M. Tovar}, Banach Cent. Publ. 37, 53--66 (1996; Zbl 0887.46006) Full Text: EuDML