Geodesic lines in Nearly K\"ahler S^3\timesS^3

TL;DR

This paper explicitly parameterizes geodesic lines in the nearly K"ahler manifold S^3×S^3, a space with a weakened K"ahler condition, expanding understanding of its geometric structure.

Contribution

It provides the first explicit parameterization of geodesic lines in the nearly K"ahler S^3×S^3 manifold, a significant step in understanding its geometry.

Findings

Explicit parameterization of geodesic lines in S^3×S^3

Enhanced understanding of nearly K"ahler geometry

Foundation for further geometric analysis

Abstract

A nearly K\"ahler manifold is an almost Hermitian manifold with the weakened K\"ahler condition, that is, instead of being zero, the covariant derivative of the almost complex structure is skew-symmetric. We give the explicit parameterization of geodesic lines on the nearly K\"ahler S^3\timesS^3.