Two classes of slant surfaces in nearly Kahler six sphere

Details Two classes of slant surfaces in nearly Kahler six sphere Two classes of slant surfaces in nearly Kahler six sphere

2010-09-27

arxiv.org/abs/1009.5369v1

Mathematics

Differential Geometry

11 pages

Scientific paper

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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