Special Einstein’s equations on Kähler manifolds

Irena Hinterleitner and Volodymyr Kiosak

Brno University of Technology, Faculty of Civil Engineering, Department of Mathematics, Žižkova 17, 602 00 Brno, Czech Republic
Odessa National Polytechnical University, Department of Informatics and Mathematical Methods of Information Systems Protection, Prosp. Shevchenko 1, 65044 Odessa, Ukraine


Abstract: This work is devoted to the study of Einstein equations with a special shape of the energy-momentum tensor. Our results continue Stepanov’s classification of Riemannian manifolds according to special properties of the energy-momentum tensor to Kähler manifolds. We show that in this case the number of classes reduces.

AMSclassification: primary 53B20; secondary 53B30, 53B35, 53B50, 32Q15, 35Q76.

Keywords: Einstein’s equations, Kähler manifolds, pseudo-Riemannian spaces, Riemannian spaces.