2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65753We prove two geometric index theorems for a family of first-order elliptic operators over a manifold with boundary by computing eta form representatives for the Chern character classes of the index bundle. The eta forms occur as relative and regularized traces on infinite-dimensional vector bundles realized as the limiting values of superconnection character forms.v2: minor changes to Sect.1 and Sect. 4 + various typos. 51 pagesDifferential Geometrytext