Angle, R. Blair Geometric properties and related results for holomorphic Segre preserving maps. (English) Zbl 1254.32004 Complex Var. Elliptic Equ. 57, No. 10, 1055-1072 (2012). Summary: We examine holomorphic Segre preserving maps between the complexifications of real analytic hypersurfaces in \(\mathbb C^{n+1}\). In particular, we find several sufficient conditions ensuring that Segre transversality and total Segre nondegeneracy of the maps must hold. Cited in 2 Documents MSC: 32A10 Holomorphic functions of several complex variables 32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables 32V40 Real submanifolds in complex manifolds 32V35 Finite-type conditions on CR manifolds Keywords:complexifications of real analytic hypersurfaces; holomorphic Segre preserving maps; Segre transversality PDFBibTeX XMLCite \textit{R. B. Angle}, Complex Var. Elliptic Equ. 57, No. 10, 1055--1072 (2012; Zbl 1254.32004) Full Text: DOI arXiv References: [1] DOI: 10.1007/BF01405151 · Zbl 0464.32011 · doi:10.1007/BF01405151 [2] Angle RB, Ph.D. thesis (2008) [3] DOI: 10.2140/pjm.2010.247.283 · Zbl 1203.32013 · doi:10.2140/pjm.2010.247.283 [4] DOI: 10.1007/s00208-006-0045-3 · Zbl 1117.32012 · doi:10.1007/s00208-006-0045-3 [5] Baouendi MS, Princeton Math. Series 47 (1999) [6] DOI: 10.1090/S0894-0347-06-00534-0 · Zbl 1112.32017 · doi:10.1090/S0894-0347-06-00534-0 [7] Kohn JJ, J. Differ. Geom. 6 pp 523– (1972) [8] DOI: 10.1007/BF01425740 · doi:10.1007/BF01425740 [9] DOI: 10.1353/ajm.1996.0005 · Zbl 0849.32012 · doi:10.1353/ajm.1996.0005 [10] DOI: 10.1353/ajm.2006.0039 · Zbl 1105.32022 · doi:10.1353/ajm.2006.0039 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.