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Weyl tensor

  1. Aug 7, 2006 #1
    Hello, I wish to show that on 3-dimensional manifolds, the weyl tensor vanishes.
    In other words, I want to show that the curvature tensor, the ricci tensor and curvature scalar hold the relation


    Please, if anyone knows how I can prove this relation or refer to a place which proves the relation, I will be most grateful.

    Thanks in advance
  2. jcsd
  3. Aug 7, 2006 #2

    jim mcnamara

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    Staff: Mentor

    You have created an identical thread in the Physics area. Please don't double post.
  4. Sep 23, 2006 #3
    Hey! Jim McNamara ......

    Excuses Excuses Jim McNamara.

    I was interested in his question. I find it obnoxious that someone that didn't even participate in providing him with an answer in the physics section has the audacity to chid him for being interested in asking a larger audience.

    In another person's post about unitary matrices you tried answering with some nonsense, that Matt grime cleaned up.

    In a post called complex.h . You again gave bogus statements that were cleaned up by Hurkyl.

    In a post Atomic number and Orbitals. You again make a God like statement about passing on answering it as you think it is someone's homework and it is incomprehensible. But others gave him a clear answer.

    In Asymptotic mathcing for a first order differential equation post . You again declare that a variable "e" in some equation must refer to Napier's constant. At least there you start with "I'M CONFUSED".

    In Sulfur Based Lifeforms Question post . You don't even get that the point is that we are carbon based life forms.

    I am not in charge of this forum. But please don't TELL anyone else anything, ok. (Especially about math, it isn't based on an opinion which you obviously want to flaunt).

  5. Sep 23, 2006 #4
    the long and short of the proof is: first show that the tensor is skew-symmetric in any two variables; then take a basis of TM and plug them into the weyl tensor; the weyl tensor is a 4-tensor, so one of the basis elements has to double up; hence it's zero.
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