Product complex sumanifold of indefinite complex space forms
An analogue of the Segre imbedding for the indefinite complex projective (and hyperbolic) space is constructed. The paper then deals with isometric holomorphic immersions of a product of two complete indefinite Kähler manifolds into a complex projective space. It is shown that the smallest possible dimension and index of such an immersion corresponds to the indefinite Segre imbedding. In the final sections the indefinite Segre imbedding is characterized in terms of parallelity of the second fundamental form, while the Segre imbedding of a product of two complex hyperbolic spaces into an indefinite complex hyperbolic space is discussed by means of the length of its second fundamental form.
scientific article; zbMATH DE number 4090303