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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 3dimensional space if necessary (distance between two points P and Q would then be Sqrt[(PQ)^T * M * (PQ)]), but I plan on integrating over spatially varying metrics as well.
Any ideas would be appreciated, victor



