BIBLIOS

Tipo
Artigos em Revista

Tipo de Documento
Artigo Completo

Título
A characterization of the standard embeddings of CP2 and Q3.

Participantes na publicação
Eschenburg, J. (Author)
Ferreira, M. J. (Author)
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA
CMAF
Tribuzy, R. (Author)

Resumo
H. Hopf showed that the only constant mean curvature sphereS2immersed inR3is the round sphere. The K ?ahler frameworkis an adequate approach to generalize Hopf’ s theorem to higherdimensions. Whenφ:M→Rnis an isometric immersion froma K ?ahler manifold, the complexified second fundamental formαsplits according to types. The (1,1) part of the second funda-mental form plays the role of the mean curvature for surfaces andwill be called the pluri-mean curvaturepmc. Therefore isometricimmersions with parallel pluri-mean curvature (ppmcisometricimmersions) generalize in a natural way the cmc immersions. Itis a standard fact thatR8is the smallest space whereCP2can beembedded. The aim of this work is to generalize Hopf’s theoremproving in particular that the onlyppmcisometric immersion fromCP2intoR8is the standard immersion.


Suporte
Journal of Differential Geometry

Identificadores da Publicação
ISSN - 0022-040X



Identificadores do Documento
DOI - https://doi.org/10.4310/jdg/1274707315