ALS in German, signed “A. Einstein,” one page, 8.5 x 10.75, no date. Handwritten letter to French physicist, Francis Perrin, the son of Nobel prize-winning physicist Jean Perrin, in full (translated): "It is quite possible that the cosmological generalization of the questions of fields that you propose will become important again when the questions closest to it have been resolved. The main interest of your result seems to me for the moment to be of a mathematical nature. Until now, it is still not known if in a spherical-like space there exist n-Bein-like fields free from singularities, especially since this is not the case in a two-dimensional space. It would be necessary to prove that the points PHI=0 and PHI=pi are regular with respect to the n-Bein field, because it does not appear clearly in your diagram. Moreover, we do not see if the space is homogeneous (if by a rotation of the space and a corresponding rotation of n-Bein, this n-Bein space is transferred into itself). It would also be interesting to know how you arrived at your interesting hsv (for the three-dimensional case). I look forward to your further explanations. Greetings to you and your father." In very good to fine condition, with light creasing and toning to the edges, and silking on the back for reinforcement.
The initial development of general relativity was in a pseudo-Riemannian setting, where you have a four-dimensional curved spacetime, a so-called manifold, and a way to measure distances, a metric. Using the fundamental metric, you can develop notions of ‘shortest’ paths between points and a way to measure geodesic deviation, which leads to a notion of connection. On the basis of curved spacetime, Einstein introduced frame fields, also called tetrads or vierbeins (a globally defined vielbein/n-bein), into general relativity in 1928, which led to the concept that he called ‘Fern-Parallelismus,’ often translated as ‘teleparallelism.’ A complex and fascinating letter from Einstein.
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