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Zur metrischen Differentialgeometrie auf den Bündeln der einfachenp-Vektoren und (n-p)-Vektoren

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Summary

A previous paper[4] shows how the connection parameters for tangent simple p-vectors of a manifold can be split into p vectors and certain definite elements γ ρh i . In this paper the ensuing differential geometry is extended to the properties of both contra- and covariant simple p- and (n-p)-vectors of this manifold. The five new invariant derivatives are proved to be similarly composed of a set of vectors and their derivatives. These allow for a simplified expression for the Gauss and Weingarten equations and consequently for the first variations of the respective areas and for the necessary minimal conditions.

Literaturverzeichnis

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    I. Haubitz,Nichlineare Zusammenhänge in Bündeln von Graßmann-Kegeln, Tensor, N. S.,24 (1972), pp. 123–160.

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    H. Iwamoto,On geometries associated with multiple integrals, Math. jap.,1 (1948), pp. 74–91.

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Entrata in Redazione il 17 dicembre 1974.

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Haubitz, I. Zur metrischen Differentialgeometrie auf den Bündeln der einfachenp-Vektoren und (n-p)-Vektoren. Annali di Matematica 109, 89–115 (1976). https://doi.org/10.1007/BF02416954

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