English

Two classes of slant surfaces in nearly Kahler six sphere

Differential Geometry 2010-09-28 v1

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 \OO.\Im \OO . Later on, we classify the slant surfaces of S6S^6 which are orbits of maximal torus in G2.G_2. We show that these orbits are flat tori which are linearly full in S5S6S^5\subset S^6 and that their slant angle is between arccos13\arccos \frac{1}{3} and π2.\frac{\pi}{2}. Among them we find one parameter family of minimal orbits.

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Cite

@article{arxiv.1009.5369,
  title  = {Two classes of slant surfaces in nearly Kahler six sphere},
  author = {K. Obrenovic and S. Vukmirovic},
  journal= {arXiv preprint arXiv:1009.5369},
  year   = {2010}
}

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11 pages