Christoffel symbols knowing Line element (check my result)

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I'm asked to find all the non-zero Christoffel symbols given the following line element:



$ds^2=2x^2dx^2+y^4dy^2+2xy^2dxdy$



The result I have obtained is that the only non-zero component of the Christoffel symbols is:



$Gamma^x_xx=frac1x$



Is this correct?



Thanks!!!




differential-geometry tensors




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    up vote
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    I'm asked to find all the non-zero Christoffel symbols given the following line element:



    $ds^2=2x^2dx^2+y^4dy^2+2xy^2dxdy$



    The result I have obtained is that the only non-zero component of the Christoffel symbols is:



    $Gamma^x_xx=frac1x$



    Is this correct?



    Thanks!!!




    differential-geometry tensors




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I'm asked to find all the non-zero Christoffel symbols given the following line element:



      $ds^2=2x^2dx^2+y^4dy^2+2xy^2dxdy$



      The result I have obtained is that the only non-zero component of the Christoffel symbols is:



      $Gamma^x_xx=frac1x$



      Is this correct?



      Thanks!!!




      differential-geometry tensors




      share|cite|improve this question











      I'm asked to find all the non-zero Christoffel symbols given the following line element:



      $ds^2=2x^2dx^2+y^4dy^2+2xy^2dxdy$



      The result I have obtained is that the only non-zero component of the Christoffel symbols is:



      $Gamma^x_xx=frac1x$



      Is this correct?



      Thanks!!!





      differential-geometry tensors





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked yesterday









      Confused Physicist

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          It's incorrect, there are more non-zero symbols. Also, in my previous answer, I thought you meant to just check the one entry you specified. Here are all the symbols. I suggest looking into CAS's if you plan to compute many symbols.



          enter image description here






          share|cite|improve this answer























          • Ohhhh Thank you so much. I've just seen my mistake. You've helped me a lot! And thanks for the code too!!
            – Confused Physicist
            yesterday










          • Can I ask you one more question? For these Christoffel symbols, are all the components of the Riemann curvature tensor zero? $R^alpha_betagammadelta$
            – Confused Physicist
            yesterday










          • @ConfusedPhysicist it's not really appropriate to have extended answers in the comments. Furthermore, I don't have the time right now to code up the RIemann tensor but I suggest, if you have Mathematica, to use GRQUICK which is here: library.wolfram.com/infocenter/MathSource/8329
            – jman
            yesterday










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          1 Answer
          1






          active

          oldest

          votes









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          oldest

          votes






          active

          oldest

          votes








          up vote
          0
          down vote



          accepted










          It's incorrect, there are more non-zero symbols. Also, in my previous answer, I thought you meant to just check the one entry you specified. Here are all the symbols. I suggest looking into CAS's if you plan to compute many symbols.



          enter image description here






          share|cite|improve this answer























          • Ohhhh Thank you so much. I've just seen my mistake. You've helped me a lot! And thanks for the code too!!
            – Confused Physicist
            yesterday










          • Can I ask you one more question? For these Christoffel symbols, are all the components of the Riemann curvature tensor zero? $R^alpha_betagammadelta$
            – Confused Physicist
            yesterday










          • @ConfusedPhysicist it's not really appropriate to have extended answers in the comments. Furthermore, I don't have the time right now to code up the RIemann tensor but I suggest, if you have Mathematica, to use GRQUICK which is here: library.wolfram.com/infocenter/MathSource/8329
            – jman
            yesterday














          up vote
          0
          down vote



          accepted










          It's incorrect, there are more non-zero symbols. Also, in my previous answer, I thought you meant to just check the one entry you specified. Here are all the symbols. I suggest looking into CAS's if you plan to compute many symbols.



          enter image description here






          share|cite|improve this answer























          • Ohhhh Thank you so much. I've just seen my mistake. You've helped me a lot! And thanks for the code too!!
            – Confused Physicist
            yesterday










          • Can I ask you one more question? For these Christoffel symbols, are all the components of the Riemann curvature tensor zero? $R^alpha_betagammadelta$
            – Confused Physicist
            yesterday










          • @ConfusedPhysicist it's not really appropriate to have extended answers in the comments. Furthermore, I don't have the time right now to code up the RIemann tensor but I suggest, if you have Mathematica, to use GRQUICK which is here: library.wolfram.com/infocenter/MathSource/8329
            – jman
            yesterday












          up vote
          0
          down vote



          accepted







          up vote
          0
          down vote



          accepted






          It's incorrect, there are more non-zero symbols. Also, in my previous answer, I thought you meant to just check the one entry you specified. Here are all the symbols. I suggest looking into CAS's if you plan to compute many symbols.



          enter image description here






          share|cite|improve this answer















          It's incorrect, there are more non-zero symbols. Also, in my previous answer, I thought you meant to just check the one entry you specified. Here are all the symbols. I suggest looking into CAS's if you plan to compute many symbols.



          enter image description here







          share|cite|improve this answer















          share|cite|improve this answer



          share|cite|improve this answer








          edited yesterday


























          answered yesterday









          jman

          1484




          1484











          • Ohhhh Thank you so much. I've just seen my mistake. You've helped me a lot! And thanks for the code too!!
            – Confused Physicist
            yesterday










          • Can I ask you one more question? For these Christoffel symbols, are all the components of the Riemann curvature tensor zero? $R^alpha_betagammadelta$
            – Confused Physicist
            yesterday










          • @ConfusedPhysicist it's not really appropriate to have extended answers in the comments. Furthermore, I don't have the time right now to code up the RIemann tensor but I suggest, if you have Mathematica, to use GRQUICK which is here: library.wolfram.com/infocenter/MathSource/8329
            – jman
            yesterday
















          • Ohhhh Thank you so much. I've just seen my mistake. You've helped me a lot! And thanks for the code too!!
            – Confused Physicist
            yesterday










          • Can I ask you one more question? For these Christoffel symbols, are all the components of the Riemann curvature tensor zero? $R^alpha_betagammadelta$
            – Confused Physicist
            yesterday










          • @ConfusedPhysicist it's not really appropriate to have extended answers in the comments. Furthermore, I don't have the time right now to code up the RIemann tensor but I suggest, if you have Mathematica, to use GRQUICK which is here: library.wolfram.com/infocenter/MathSource/8329
            – jman
            yesterday















          Ohhhh Thank you so much. I've just seen my mistake. You've helped me a lot! And thanks for the code too!!
          – Confused Physicist
          yesterday




          Ohhhh Thank you so much. I've just seen my mistake. You've helped me a lot! And thanks for the code too!!
          – Confused Physicist
          yesterday












          Can I ask you one more question? For these Christoffel symbols, are all the components of the Riemann curvature tensor zero? $R^alpha_betagammadelta$
          – Confused Physicist
          yesterday




          Can I ask you one more question? For these Christoffel symbols, are all the components of the Riemann curvature tensor zero? $R^alpha_betagammadelta$
          – Confused Physicist
          yesterday












          @ConfusedPhysicist it's not really appropriate to have extended answers in the comments. Furthermore, I don't have the time right now to code up the RIemann tensor but I suggest, if you have Mathematica, to use GRQUICK which is here: library.wolfram.com/infocenter/MathSource/8329
          – jman
          yesterday




          @ConfusedPhysicist it's not really appropriate to have extended answers in the comments. Furthermore, I don't have the time right now to code up the RIemann tensor but I suggest, if you have Mathematica, to use GRQUICK which is here: library.wolfram.com/infocenter/MathSource/8329
          – jman
          yesterday












           

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