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A New Viewpoint in Differential Geometry

Published online by Cambridge University Press:  20 November 2018

S. Bochner
S. Bochner*
Affiliation:
Princeton University
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The law of transformation for a general mixed tensor

1

is somewhat complicated at first sight, but algebraically it can be stated succinctly in the following manner. If, without regard to the original position of various indices, we denote the components of the tensor in some fixed simple ordering by

2

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 460 - 470
Copyright
Copyright © Canadian Mathematical Society 1951

References

1 See our papers: Vector fields and Ricci-curvature, Bull. Amer. Math. Soc, vol. 52 (1946), 776-797, and Curvature and Betti numbers, Ann. of Math., vol. 49 (1948), 379-390 and II in vol. 50 (1949), 77-93.

2 Vector fields on complex and real manifolds, Ann. of Math. vol. 52 (1950), 642-649.