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symmetries of euclidean space

  • To: mathgroup at smc.vnet.net
  • Subject: [mg116504] symmetries of euclidean space
  • From: gmoutso <gmoutso at googlemail.com>
  • Date: Thu, 17 Feb 2011 05:19:39 -0500 (EST)

Hi,
I am puzzled about the following problem.

Flat spacetime ds^2=dx^2+dy^2 has 3 symmetries: two translations and
one rotation. When I attempt to solve the Killing vector equation in
mathematica

DSolve[ {D[T[t, x], x] + D[X[t, x], t] == 0, D[T[t, x], t] == 0,
  D[X[t, x], x] == 0}, {T[t, x], X[t, x]}, {t, x}]

I get

DSolve::overdet: There are fewer dependent variables than equations,
so the system is overdetermined.

What's the way of going about this (e.g. in the case of a d-
dimensional curved metric when the solution if any is not obvious)?

Thanks,
George


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