Abstract
Over all indices which appear twice on the right hand expression, once as subscript and once as superscript. Further on, the summation sign will be omitted in tensor calculus, but not in exterior calculus for reasons becoming evident below, and Einstein’s summation convention will be used which means the just described summation over pairs of indices always understood.
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References
Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry. Interscience, vols. I and II. New York (1963 and 1969)
Warner, F.W.: Foundations of Differentiable Manifolds and Lie Groups. Springer, New York (1983)
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Eschrig, H. (2010). Tensor Fields. In: Topology and Geometry for Physics. Lecture Notes in Physics, vol 822. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14700-5_4
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DOI: https://doi.org/10.1007/978-3-642-14700-5_4
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