Gauss maps of harmonic and minimal great circle fibrations
Gauss maps of harmonic and minimal great circle fibrations
Abstract We investigate Gauss maps associated to great circle fibrations of the euclidean unit 3-sphere $$\mathbb {S}^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> . We show that the associated Gauss map to such a fibration is harmonic, respectively minimal, if and only if the unit vector field …