Two classes of slant surfaces in nearly Kahler six sphere

K. Obrenovic; S. Vukmirovic

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arXiv · 1009.5369

Two classes of slant surfaces in nearly Kahler six sphere

K. Obrenovic·S. Vukmirovic

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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 $\Im \OO .$ 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 $\arccos \frac{1}{3}$ and $\frac{\pi}{2}.$ Among them we find one parameter family of minimal orbits.

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K. Obrenovic, S. Vukmirovic. 2010-09-27. Two classes of slant surfaces in nearly Kahler six sphere. https://arxiv.org/abs/1009.5369

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