Two classes of slant surfaces in nearly Kahler six sphere
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 o...
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Zusammenfassung: | 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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DOI: | 10.48550/arxiv.1009.5369 |