(adsbygoogle = window.adsbygoogle || []).push({}); "Discrete" Geommetry...

-What can you do if you have a "Smooth" Manifold..but it's very hard to work with?..perhaps you could "discretize" the surface splitting it into "triangles" and take the basic coordinates to be the angles (3) of every triangle..but my question is What would happen with the Metric the "ricci Tensor" (Riemann Tensor contracted ?) and other Differential Geommetry identities?.. How could you recover them or calculate them approximately?..thanks.

- for example an idea applied to Gr you have the Einstein Hamiltonian..if you discretize it using the angles of every "triangle" you would have:

[tex] L= \sqrt (-g) R \rightarrow L( \theta_i (t), \dot \theta_i (t),t) [/tex] for i=1,2,3,4,5,6,7,8,9,........... From this Lagrangian i could obtain the Hamiltonian and hence the "Energy levels"...but I'm missing [tex] R_{ab} [/tex] and metric Tensor...How could i achieve the problem.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Discrete Geommetry

**Physics Forums | Science Articles, Homework Help, Discussion**