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