Isoparametric surfaces and the tt*-equations

Abstract

In this paper we provide a link between tt*-bundles, which are solutions of a general version of the equations of topological–antitopological fusion considered by Cecotti–Vafa, Dubrovin and Hertling and isoparametric spherical surfaces, i.e. spherical surfaces with constant principal curvatures. More precisely, we construct a tt*-bundle from a pluriharmonic map into the hermitian symmetric space S O ( l + 2 ) / S O ( 2 ) × S O ( l ) which can be seen as the Grassmannian G r ( 2 , n + 2 ) of oriented two-planes in R n + 2 . Applying the above construction to the Gauss map of an isoparametric spherical surface we associate to a given isoparametric spherical surface a new solution to the t t ∗ -equations.