Two classes of slant surfaces in nearly Kahler six sphere

zbMATH Open1280.53059arXiv1009.5369MaRDI QIDQ2871821

K. Obrenović, Srdjan Vukmirović

Publication date: 10 January 2014

Abstract: In this paper we find examples of slant surfaces in the nearly Kahler six sphere. First, we characterize two-dimensional small and great spheres which are slant. Their description is given in terms of the associative 3-form in $ImOO.$ Later on, we classify the slant surfaces of $S^6$ which are orbits of maximal torus in $G_2.$ We show that these orbits are flat tori which are linearly full in $S^{5}subset{S}^6$ and that their slant angle is between $arccosfrac13$ and $fracpi2.$ Among them we find one parameter family of minimal orbits.

Full work available at URL: https://arxiv.org/abs/1009.5369

zbMATH Keywords

Kähler angleoctonionsslant surfacessix sphere

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

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