English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the zaia usage as premium feature

ZAIA

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the access of premium content as premium feature

Premium Content

Zendy Tools

Zendy Open

In the last years, the use of an idea of A. Ros, [11], has meant an interesting progress in the study of several families of submanifoids of the complex projective space CPn. This idea essentially consists in considering the firststandard embedding of CPn in a certain Euclidean space RN, and contemplating the submanifoids of CPn in the light of that new embedding. The firststandard embedding has parallel second fundamental form and makes CPn to be a symmetric i?-space in RN. In particular real hypersurfaces of CPn have been analysed under this point of view, [6], [13], and new characterizations of this important class of hypersurfaces have been obtained. In 1986, the second author and S. Montiel, [8], made a systematic study of a certain family of real hypersurfaces of the complex hyperbolic space CHn. In the process of classificationof that family they introduced new examples without parallelin CPn. Therefore if we could get an isometric embedding of CHn in some Euclidean space RN provided of as good geometric properties as those of the firststandard embedding of CPn, we could try to profound in the study of real hypersurfaces in CHn. On the other hand fully immersed complete submanifoids of a Euclidean space with parallel second fundamental form have been totally classifiedby D. Ferus, [3], [4]. As a consequence his result implies that a complete irreducible (as a Riemannian manifold) submanifold which is fullyimmersed in an Euclidean space with parallel second fundamental form is congruent to either an hyperplane or to an irreducible symmetric i?-space immersed by means of its standard embedding. Consequentely we see that there exist no an isometric immersion

An isometric embedding of the complex hyperbolic space in a pseudo-euclidean space and its application to the study of real hypesurfaces