Purely Real Surfaces in Non-Flat ComplexSpace Forms Satisfying a Basic Equality

摘要

An isometric immersion Φ: M Mof a manifoldMinto Kahlermanifold is called purely real if the complex structure J on M carries thetangent bundle of M into a transversal bundle. In an earlier article, the firstauthor discovered a general optimal inequality for purely real surfaces in acomplex space form M~2(4ε). He also studied purely real surfaces in C~2sat-isfying the equality case of the inequality and obtained some classificationtheorems. In this article, we classify three families of purely real surfaces innon-flat complex space forms M~r (4ε) which satisfy the equality case of theinequality.