On purely real surfaces in Kaehler surfaces and Lorentz surfaces in Lorentzian Kaehler surfaces

Abstract

An immersion $\varphi :M\to \tilde{M}$ of a manifold $M$ into an indefinite Kaehler manifold $\tilde{M}$ is called purely real if the almost complex structure $J$ on $\tilde{M}$ carries the tangent bundle of $M$ into a transversal bundle. In this article we survey some recent results on purely real surfaces in Kaehler surfaces as well as on Lorentz surfaces in Lorentzian Kaehler surfaces.

arXiv comment28 pages. Proceeding of the International Conference RIGA-2008, Brasov, Romania, July 8-11, 2008