2005/11/30 by Frederic P. Schuller, Frederic P Schuller, Mattias N. R. Wohlfarth +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math.DG
paper · pdf · doi:10.1088/1126-6708/2006/02/059
published as JHEP0602:059,2006 · 20 pages, no figures, improved journal version
openalex publication_date 2006/02/22 · arxiv created 2006/02/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
String 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.