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GR: Gravitation und Relativitätstheorie
GR 12: Einstein Modified and/or Quantized
GR 12.2: Vortrag
Donnerstag, 18. März 1999, 16:40–17:00, AM1
Discrete (Pseudo-)Riemannian Geometry — •Folkert Müller-Hoissen1 and Aristophanes Dimakis2 — 1Max-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.)