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Geometry in *COMPLEX* spaces

  1. Feb 22, 2009 #1
    I am not familiar with that stuff, so please dont laugh.

    I know some facts about the geometry when coordinates are real. In pseudo-euclidean spaces (like in special relativity) T is also real, just the definitions of a distance is different.

    R^2 = X^2+Y^2+Z^2 - T^2

    But we can say that it is an euclidean space, but T is imaginary. So, if we assume that coordinates are complex, the only difference between euclidaen space and Minkowsky space is an orientation of a subset in a 4-dimensional complex space.

    So far I hope it is correct.

    My question is, what about General relativity and curved spaces? I read that for 3space+1time curved space can be put into 86 dimensional manifold with 3 timelike dimensions.

    What if we work completely in the complex area, so there is no difference between space and time dimensions?
  2. jcsd
  3. Feb 23, 2009 #2


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    uhh? 86? :confused:

    did you get this from http://www.eng.uah.edu/~jacksoa/literature/MD_Int2.pdf? [Broken] … 86 was just an academic example … it could have been 42 or 717 or … :wink:
    Last edited by a moderator: May 4, 2017
  4. Feb 23, 2009 #3


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  5. Feb 23, 2009 #4
    it is from here: https://www.physicsforums.com/showthread.php?t=290098

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