Pracì Mìžnarodnogo Geometričnogo Centru (Jan 2024)

Conformal recurrent Kӓhler spaces

  • Olexandr Savchenko,
  • Tetyana Shevchenko,
  • Sergiy Hedulian

DOI
https://doi.org/10.15673/pigc.v17i1.2752
Journal volume & issue
Vol. 17, no. 1
pp. 88 – 98

Abstract

Read online

In this paper we study pseudo-Riemannian spaces with recurrent tensor of conformal curvature, which admit a Kähler structure. It is proved that Kähler conformally recurrent spaces other than recurrent spaces do not exist, if their dimension is four. Recurrent Kähler spaces are divided into two types. For each type, the internal necessary characteristic is given. Some properties of four-dimensional Kähler conformally recurrent Kähler spaces are studied.

Keywords