Abstract
We survey some of the fundamental classification results on low-type submanifolds of non-at 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.
Original language | English (US) |
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Pages (from-to) | 439-455 |
Number of pages | 17 |
Journal | REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES |
Volume | 65 |
Issue number | 4 |
State | Published - 2020 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics