2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173760The purpose of this paper is twofold. One is to give a survey of our study on the reductions of harmonic bundles, and the other is to explain a simple application in the study of TERP structure. In particular, we investigate the asymptotic behaviour of the "new supersymmetric index" for variation of pure polarized TERP structures.Differential GeometryComplex Variables32L05, 14D07text