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Theory and applications of abstract normal coordinates in a general differential geometry. (English) JFM 64.1369.01
Verf. beweisen zuerst einen Satz über die Differenzierbarkeit der Lösung \(\varphi(x_0,\, \xi_0, \, s)\) einer gewissen Differentialgleichung zweiter Ordnung \[ \frac{d^2\, x}{ds^2}=H \left( x, \frac{dx}{ds} \right), \] die den Anfangsbedingungen \[ (\varphi(x_0,\, \xi_0, \, s))_{s=0}=x_0, \quad \left( \frac{\partial \varphi(x_0,\, \xi_0, \, s)}{\partial s} \right)_{s=0}=\xi_0 \] unterworfen ist. Durch Anwendung dieses Satzes werden Normal-Koordinaten in einer abstrakten Differentialgeometrie mit einer linearen Übertragung eingeführt. Es werden einige Anwendungen dieser Normal-Koordinaten entwickelt und analoge Folgerungen wie in der \(n\)-dimensionalen Differentialgeometrie gezogen.

Subjects:
Zweiter Halbband. Fünfter Abschnitt. Geometrie. Kapitel 6. Differentialgeometrie. E. Differentialgeometrie in allgemeinen Räumen. Feldtheorie.
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References:
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