On purely real surfaces in Kaehler surfaces and Lorenz surfaces in Lorenzian Kaehler surfaces

Bang-Yen Chen

Authors

Bang-Yen Chen Michigan State University, U.S.A.

Keywords:

Purely real surfaces, fundamental equations, minimal surface, Lorentz surface, Kaehler surface, Lorentzian Kaehler surface, parallel surface, optimal inequality

Abstract

An immersion ϕ: M → M̃ of a manifold M into an indefinite Kaehler manifold M̃ is called purely real if the almost complex structure J on M̃ 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.