The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics » geometry.research

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Victor Liu

Posts: 1
From: Stanford
Registered: 1/3/08
using metric tensors
Posted: Jan 3, 2008 8:05 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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,

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.