Hopf hypersurfaces of low type in non-flat complex space forms
Autor: | Ivko Dimitrić |
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Jazyk: | angličtina |
Rok vydání: | 2011 |
Předmět: |
Mathematics - Differential Geometry
Pure mathematics Mean curvature flow Mean curvature Euclidean space General Mathematics 53C40 Hermitian matrix Projection (linear algebra) Algebra Differential Geometry (math.DG) Complex space FOS: Mathematics Embedding Mathematics::Differential Geometry Laplace operator Mathematics |
Zdroj: | Kodai Math. J. 34, no. 2 (2011), 202-243 |
Popis: | We classify Hopf hypersurfaces of non-flat complex space forms CP^m(4) and CH^m(-4), denoted jointly by CQ^m(4c), that are of 2-type in the sense of B. Y. Chen, via the embedding into a suitable (pseudo) Euclidean space of Hermitian matrices by projection operators. This complements and extends earlier classifications by Martinez-Ros (minimal case) and Udagawa (CMC case), who studied only hypersurfaces of CP^m and assumed them to have constant mean curvature instead of being Hopf. Moreover, we rectify some claims in Udagawa's paper to give a complete classification of constant-mean-curvature-hypersurfaces of 2-type. We also derive a certain characterization of CMC Hopf hypersurfaces which are of 3-type and mass-symmetric in a naturally defined hyperquadric containing the image of CQ^m(4c) via these embeddings. The classification of such hypersurfaces is done in CQ^2(4c), under an additional assumption in the hyperbolic case that the mean curvature is not equal to 2/3. In the process we show that every standard example of class B in CQ^m(4c) is mass-symmetric and we determine its Chen-type. Comment: 37 pages |
Databáze: | OpenAIRE |
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