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- Title
CHEN TYPE OF SOME CLASSES OF CR-SUBMANIFOLDS IN CP<sup>m</sup> AND CH<sup>m</sup>.
- Authors
DIMITRIĆ, IVKO
- Abstract
We survey some of the fundamental classification results on low-type submanifolds of non-flat model complex space forms (complex projective and hyperbolic spaces) via the standard embeddings by projection operators. These results include classification of submanifolds of type 1 in these spaces, of CMC and Hopf hypersurfaces of type 2, and investigation of the Chen type of totally real and Kähler submanifolds. Some examples of submanifolds of type 3 are presented. We also give some nonexistence results for certain families of CR-submanifolds of complex space forms of Chen type two. For example, there exist no holomorphic submanifolds of the complex hyperbolic space which are of type 2 via the standard embedding by projectors. This is contrasted with the situation in the complex projective space, where there exist some parallel Einstein Kähler submanifolds of type 2.
- Subjects
SUBMANIFOLDS; DIFFERENTIAL geometry; MANIFOLDS (Mathematics); H-spaces; HYPERSURFACES
- Publication
Revue Roumaine de Mathematiques Pures et Appliquees, 2020, Issue 4, p439
- ISSN
0035-3965
- Publication type
Article