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Topic: using metric tensors
Replies: 2   Last Post: Jan 4, 2008 11:16 AM

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 Victor Liu Posts: 1 From: Stanford Registered: 1/3/08
using metric tensors
Posted: Jan 3, 2008 8:05 PM

Hi, this is a differential geometry question, so I don't know if it belongs here.

My question is related to actual computation with metric tensors (integrals over simplices, to be precise). Given a metric tensor M (picture a 3x3 matrix, ds^2 = M_{ij} dx_i wedge dx_j) and two points in space, the metric distance between them is just the integral of the usual arc length element ds along a path. I would like to know the analogous way of computing area between three points, and volume between four points.

In particular, assume a spatially constant metric in 3-dimensional space if necessary (distance between two points P and Q would then be Sqrt[(P-Q)^T * M * (P-Q)]), but I plan on integrating over spatially varying metrics as well.

Any ideas would be appreciated,
-victor

Date Subject Author
1/3/08 Victor Liu
1/3/08 Xipan Xiao
1/4/08 Ralph Hertle