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liyiontheway
  • Member for 7 months
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  • Los Angeles, CA, United States
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Conventions for Riemann curvature tensor
@DeaneYang $R(e_k,e_l)e_j = R^i_{jkl}e_i$ is also the convention for indices of Riemann tensor preferred in Physics. $R(e_k,e_l)$ is a linear operator in the tangent space, so we put indices k and l together as a pair, and indices i and j as the matrix indices for the linear operator.
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