Important scientific manuscript written in the hand of Albert Einstein in German, unsigned, one page, 8.5 x 1, no date circa 1945. A draft variant of page 8 of the manuscript of 'Auf die Theorie metrischer komplexer Raume gegründete Feldtheorie' ('A Field Theory Based on the Theory of Complex Metric Spaces'), the initial version of the article 'A Generalization of the Relativistic Theory of Gravitation,’ published in Annals of Mathematics, Vol. 46 (Oct. 1945), pp. 578-584. The manuscript consists of a demonstration of the densities of vectors and tensors and includes many formulas and equations. It begins as follows: “Damit ist die kovariante Differentiation der Tensoren festgelegt. Wir wollen die kovariante Differentiation auch auf Tensordichten definieren” [“This defines the covariant differentiation of tensors. We also want to define the covariant differentiation on tensor densities.”] In differential geometry, the Einstein tensor, also known as the trace-reversed Ricci tensor, is used to express the curvature of a pseudo-Riemannian manifold. In general relativity, it occurs in the Einstein field equations for gravitation that describe spacetime curvature in a manner that is consistent with conservation of energy and momentum. In fine condition.
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