Two classes of slant surfaces in nearly Kahler six sphere

TL;DR

This paper classifies and describes specific slant surfaces in the nearly Kahler six sphere, including characterizations of small and great spheres and orbit structures of maximal tori, revealing their geometric properties and minimal examples.

Contribution

It provides a classification of slant surfaces in the nearly Kahler six sphere, including characterizations and descriptions of their geometric structures and minimal orbit families.

Findings

Characterization of slant small and great spheres via associative 3-form

Classification of slant surfaces as orbits of maximal tori in G_2

Identification of a family of minimal slant orbits

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.