Two classes of slant surfaces in nearly Kahler six sphere

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.

arXiv comment11 pages