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Thread: hypersurfaces of minkowski space

  1. #1 hypersurfaces of minkowski space 
    Junior Member
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    hello evebody
    I have a question if it possible.
    Given a De Sitter hypersurfaces ( in minkowski space of course), I want to know if this hypersurfaces is of constant higher order mean curvature and I want to define a Killing vectorr field to this hypersurface, For example if I take the constant vector field is this a killing vector field on this hypersurfaces.
    Other question, could you give me other example of constant higher mean curvature hypersurface in Minkowski space.
    Thanks
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  2. #2  
    Administrator Markus Hanke's Avatar
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    Quote Originally Posted by aboutammam View Post
    Given a De Sitter hypersurfaces ( in minkowski space of course), I want to know if this hypersurfaces is of constant higher order mean curvature
    The ( constant time ) hypersurfaces of Minkowski space-time are just ordinary 3-space. Since the Riemann tensor vanishes everywhere in Minkowski space-time, these hypersurfaces are all flat.

    and I want to define a Killing vectorr field to this hypersurface
    The Killing vectors are those vector fields which preserve the metric; on your ( Euclidean ) hypersurfaces, this would be translations ( 3 components ), and rotations ( also 3 components ).
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