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What is Minkowski metric?

  1. Jun 22, 2010 #1
    If a Minkowski metric is just a constant Riemann metric? I am confused with the concept in the Finsler geometry,there Minkowski metric is defined as g=g_{ij}(y)dx^idx^j.
  2. jcsd
  3. Jun 22, 2010 #2


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    Riemannian metric: An inner product on each tangent space

    Lorentzian metric: A symmetric non-degenerate bilinear form on each tangent space. (Same thing as an inner product except that <x,x> can be negative).

    Minkowski metric: A specific Lorentzian metric on [itex]\mathbb R^4[/itex] with the standard manifold structure. The metric can be defined using the identity map I as a coordinate system. Define [itex]\langle x,y\rangle=x^T\eta y[/itex], where [itex]\eta[/itex] is the diagonal 4×4 matrix with -1,1,1,1 (or 1,-1,-1,-1) on the diagonal, the x and y on the left are tangent vectors, and the x and the y on the right are 4×1 matrices with components equal to the components of those tangent vectors in the "coordinate system" I.

    Finsler metric: A norm on each tangent space.
    Last edited: Jun 22, 2010
  4. Jun 22, 2010 #3
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