Lipschitz minimality of the multiplication maps of unit complex, quaternion and octonion numbers

Abstract

We prove that the multiplication maps $s^n\times s^n\to s^n$ ($n=1,3,7$) for unit complex, quaternion and octonion numbers are, up to isometries of domain and range, the unique Lipschitz constant minimizers in their homotopy classes. Other geometrically natural maps, such as projections of Hopf fibrations, have already been shown to be, up to isometries, the unique Lipschitz constant minimizers in their homotopy classes, and it is suspected that this may hold true for all Riemannian submersions of compact homogeneous spaces.

13 pages with 3 figures

References in corpus (1)

• Lipschitz minimality of Hopf fibrations and Hopf vector fields

Cited by in corpus (1)

• Volume distortion in homotopy groups