Minimal surfaces in a complex hyperquadric \(Q _{2}\) (Q1942242)
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scientific article; zbMATH DE number 6145952
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Minimal surfaces in a complex hyperquadric \(Q _{2}\) |
scientific article; zbMATH DE number 6145952 |
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Minimal surfaces in a complex hyperquadric \(Q _{2}\) (English)
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18 March 2013
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In the paper, \(Q_2 = \mathrm{SO}(4)/\mathrm{SO}(2)\times \mathrm{SO}(2)\) denotes a hyperquadric in \({\mathbb CP^3}\). Minimal surfaces in \(Q_2\) are studied. The main results state that (1) a minimal surface in \(Q_2\) with constant Kähler angle is either holomorphic, or anti-holomorphic, or totally real (Theorem 3.1) and (2) a conformally embedded minimal sphere \(S^2\subset Q_2\) is totally geodesic provided that it has either constant sectional curvature or parallel second fundamental form (Theorem 4.1).
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minimal surface
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complex projective space
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hyperquadric
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