Local equivalence of some maximally symmetric (2,3,5)-distributions III: An-Nurowski surface rolling on a plane

2023/05/02 by Randall, Matthew
#53C18 #58A15 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.01391

Abstract

We consider the maximally symmetric (2,3,5)-distribution given by the An-Nurowski circle twistor bundle over the product of an An-Nurowski surface and the plane. This circle twistor distribution encodes the configuration space of an An-Nurowski surface rolling without slipping or twisting on the plane. We calculate the vector fields associated to this maximally symmetric (2,3,5)-distribution that define a split \frakg₂ Lie algebra and by projection we obtain an action of SL(3,ℝ) on the submanifold ℝ²× \mathbbS¹ (the configuration space without a surface).

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