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Heidelberg 1999 – scientific programme

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GR: Gravitation und Relativitätstheorie

GR 12: Einstein Modified and/or Quantized

GR 12.2: Talk

Thursday, March 18, 1999, 16:40–17:00, AM1

Discrete (Pseudo-)Riemannian Geometry — •Folkert Müller-Hoissen1 and Aristophanes Dimakis21Max-Planck-Institut für Strömungsforschung, Bunsenstrasse 10, D-37073 Göttingen — 2Mathematics Department, GR-83200 Karlovasi, Samos, Greece

Within a framework of noncommutative geometry, we introduce a formalism of discrete geometry which is very much analogous to continuum (pseudo-) Riemannian geometry. It is based on a correspondence between first order differential calculi on a discrete set and digraphs (connecting the points of the set). On a differential calculus one can then introduce metrics, compatible linear connections, and other counterparts of geometric structures of continuum Riemannian differential geometry. In the case of a differential calculus which corresponds to a hypercubic lattice digraph, we propose an new discrete version of Einstein’s equations.
Ref.: gr-qc/9808023 (to appear in J. Math. Phys.)

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