Product complex sumanifold of indefinite complex space forms
type: Item
instance of: scholarly article
title: Product complex sumanifold of indefinite complex space forms
zbMATH Open document ID: 0666.53033
DOI: 10.1216/RMJ-1988-18-3-601
author: Toshihiko Ikawa
author: Hisao Nakagawa
author: Alfonso Romero
published in: Rocky Mountain Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 4090303
zbMATH Keywords: indefinite complex projective space
zbMATH Keywords: Segre imbedding
zbMATH Keywords: isometric holomorphic immersions
zbMATH Keywords: second fundamental form
zbMATH Keywords: complex hyperbolic spaces
reviewed by: Liviu Ornea
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4090303