WebJul 11, 2024 · But the expression that I am getting through first principles is the one above. However Schutz mentions towards the end of the chapter that for a non-coordinate basis the definition of the Christoffel symbol changes and hence the one that was used to derive the above is only valid for coordinate basis in which the partial derivatives can be ... WebJun 29, 2012 · The Christoffel symbols are arrays of real numbers. They are dimensionless. Why do you say this? Since the metric tensor is dimensionless, and the Christoffel symbols are the derivatives of the metric tensor with respect to the coordinates, shouldn't the Christoffel symbols have dimensions of 1/length? Jun 20, 2012 #4 Homework Helper …
Christoffel
WebDec 1, 2024 · The first way is by calculating the Christoffel symbols and from that construct the Riemann tensor (the painful way). The second way is by using the simple definition, i.e. R i j k l = k ( g i k g j l − g i l g j k). It turns out that the expression you get from the painful way simplifies to the simple definition. Share Cite Improve this answer WebOct 21, 2024 · 1. Accordingly to historical E.B. Christoffel’s work (I think year 1869), (Christoffel’s) symbols are symmetric in the two (today writing) lower indices. 2. These symbols have been introduced when studying the preservation of … da judgment\u0027s
David Christoffel Obituary (1976-2010) - Blue Ridge, TX
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