Three-dimensional minimal CR submanifolds in \(S^{6}\) satisfying Chen's equality

DOI10.1016/j.geomphys.2005.12.002zbMath1103.53028OpenAlexW2069980199MaRDI QIDQ2507874

Luc Vrancken, Mirjana Djoric

Publication date: 5 October 2006

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2005.12.002

zbMATH Keywords

minimal submanifoldChen's equalityCR submanifoldnearly Kähler 6-sphere

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Local submanifolds (53B25)

Related Items (12)

Minimal contact CR submanifolds in \(\mathbb S^{2n+1}\) satisfying the \(\delta(2)\)-Chen equality ⋮ Three-dimensional minimal CR submanifolds of the sphere \(S^6(1)\) contained in a hyperplane ⋮ \(\delta^{\sharp}(2,2)\)-ideal centroaffine hypersurfaces of dimension 4 ⋮ On strongly minimal Kähler surfaces in \(\mathbb{C}^3\) and the Equality \(\mathrm{scal}(p) = 4 \inf \mathrm{sec}(\pi^r)\) ⋮ Geometric conditions on three-dimensional CR submanifolds in S ⁶ ⋮ \(\delta^{\sharp}(2,2)\)-ideal centroaffine hypersurfaces of dimension 5 ⋮ CR submanifolds of the nearly Kähler \(\mathbb {S}^3\times \mathbb {S}^3\) characterised by properties of the almost product structure ⋮ On certain contact 𝐶𝑅-submanifolds in 𝕊⁷ ⋮ CR-Submanifolds of the Nearly Kähler 6-Sphere ⋮ Ruled three-dimensional CR submanifolds of the sphere S6(1) ⋮ Three-Dimensional CR Submanifolds in $S^6(1)$ with Umbilical Direction Normal to $\mathcal{D}_3$ ⋮ Classification of ideal submanifolds of real space forms with type number \(\leq 2\)

Cites Work

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• Characterizing a class of totally real submanifolds of \(S^ 6\) by their sectional curvatures
• On problems of U. Simon concerning minimal submanifolds of the nearly Kaehler 6-sphere
• Totally Real Submanifolds in a 6-Sphere
• ON ALMOST COMPLEX CURVES IN THE NEARLY KÄHLER 6-SPHERE
• Totally Real Minimal Surfaces with Non-Circular Ellipse of Curvature in the Nearly Kähler S ⁶
• On some 3-dimensional CR submanifolds inS⁶
• Totally real submanifolds in $S^6(1)$ satisfying Chen’s equality
• Almost Complex Submanifolds of the Six Sphere

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