On purely real surfaces in Kähler surfaces and Lorentz surfaces in Lorenzian Kähler surfaces (Q2866246)

Let \(\varphi:M\rightarrow\tilde{M}\) be an immersion of a manifold \(M\) into an indefinite Kähler manifold \((\tilde M, J)\). Then \(\varphi\) is called ``purely real'' if the almost complex structure \(J\) transforms the tangent bundle \(TM\) into a transversal bundle, i.e., \(J(TM)\cap TM=\{0\}\); hence \(\varphi\) does not contains complex points.NEWLINENEWLINENEWLINEThe present paper is an excellent survey on the theory of this type of immersions. A special view is towards Lorentz surfaces in Lorentzian Kähler surfaces.