On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds

Irena Hinterleitner and Josef Mikeš

Address:
I. Hinterleitner, Brno University of Technology, Faculty of Civil Engineering, Department of Mathematics, Žižkova 17, 602 00 Brno, Czech Republic
J. Mikeš Palacky University, Department of Algebra and Geometry, 17. listopadu 12, 771 46 Olomouc, Czech Republic

E-mail:
hinterleitner.irena@seznam.cz
josef.mikes@upol.cz

Abstract: In this paper we study fundamental equations of holomorphically projective mappings from manifolds with equiaffine connection onto (pseudo-) Kähler manifolds with respect to the smoothness class of connection and metrics. We show that holomorphically projective mappings preserve the smoothness class of connections and metrics.

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

Keywords: holomorphically projective mapping, smoothness class, Kähler manifold, manifold with affine connection, fundamental equation.

DOI: 10.5817/AM2013-5-295