Closed conformal vector fields and Lagrangian submanifolds in complex space forms. (Q1858141)

In this paper, a family of Lagrangian submanifolds in non flat complex space forms is studied. Such submanifolds are called pseudoumbilical and determined by the property of admitting a closed and conformal vector field \(X\) such that this vector field is a principal direction of the shape operator \(A_{JX}\), where \(J\) is the complex structure of the ambient manifold. In this family, the different global characterizations of the Whitney spheres in the complex projective and hyperbolic space are also given.