2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/182872String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate differential geometric structure which is of relevance for the minimal surface equation in such a generalized geometry. In particular the notion of a derivative action of areas on areas emerges naturally. Area metric geometry provides new tools in differential geometry, which promise to play a role in the description of gravitational dynamics on D-branes.20 pages, no figures, improved journal versionHigh Energy Physics - TheoryGeneral Relativity and Quantum CosmologyDifferential Geometrytext