BIBLIOS

Document type
Journal articles

Document subtype
Full paper

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

Participants in the publication
Eschenburg, J. (Author)
Ferreira, M. J. (Author)
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA
CMAF
Tribuzy, R. (Author)

Summary
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.


Where published
Journal of Differential Geometry

Publication Identifiers
ISSN - 0022-040X



Document Identifiers
DOI - https://doi.org/10.4310/jdg/1274707315