On holomorphically projective mappings of $e$-Kähler manifolds

Irena Hinterleitner

Address: Brno University of Technology, Faculty of Civil Engineering, Department of Mathematics, Žižkova 17, 602 00 Brno, Czech Republic

E-mail: hinterleitner.irena@seznam.cz

Abstract: In this paper we study fundamental equations of holomorphically projective mappings of $e$-Kähler spaces (i.e. classical, pseudo- and hyperbolic Kähler spaces) with respect to the smoothness class of metrics. We show that holomorphically projective mappings preserve the smoothness class of metrics.

AMSclassification: primary 53B20; secondary 53B21, 53B30, 53B35, 53C26.

Keywords: holomorphically projective mappings, smoothness class, Kähler space, hyperbolic Kähler space.

DOI: 10.5817/AM2012-5-333