caa a22 4500 469117230 CHVBK 20180323133128.0 cr unu---uuuuu 170328e19920101xx s 000 0 eng 10.1007/BF02921332 doi (NATIONALLICENCE)springer-10.1007/BF02921332 Remarks on the generic rank of a CR mapping [Elektronische Daten] [M. Baouendi, Linda Rothschild] We study germs of smooth CR mappings between embedded real hypersurfaces in complex spaces of the same dimension. In particular, we are interested in the generic rank of such mappings. IfH:M →M′ is a CR map between two hypersurfacesM andM′, we prove that ifM′ does not contain any germ of a holomorphic manifold then eitherH is constant or the generic rank ofH is odd. We also prove that if there is no formal holomorphic vector field tangent toM, then eitherH is constant or genericallyH is a local diffeomorphism. It follows, as a special case, that ifM andM′ are of D-finite type (in the sense of D'Angelo) thenH is either constant or is generically a local diffeomorphism. Mathematica Josephina, Inc., 1992 CR mapping nationallicence D-finite type nationallicence essentially finite hypersurface nationallicence formal hypersurface nationallicence real hypersurface nationallicence Baouendi M. Department of Mathematics, University of California at San Diego, 92093, La Jolla, CA, USA aut Rothschild Linda Department of Mathematics, University of California at San Diego, 92093, La Jolla, CA, USA aut The Journal of Geometric Analysis Springer-Verlag 2/1(1992-01-01), 1-9 1050-6926 2:1<1 1992 2 12220 https://doi.org/10.1007/BF02921332 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02921332 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Baouendi M. Department of Mathematics, University of California at San Diego, 92093, La Jolla, CA, USA aut NATIONALLICENCE 700 1- Rothschild Linda Department of Mathematics, University of California at San Diego, 92093, La Jolla, CA, USA aut NATIONALLICENCE 773 0- The Journal of Geometric Analysis Springer-Verlag 2/1(1992-01-01), 1-9 1050-6926 2:1<1 1992 2 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer