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Zeitschrift für Analysis und ihre Anwendungen

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Volume 16, Issue 1, 1997, pp. 73–81
DOI: 10.4171/ZAA/750

Published online: 1997-03-31

Some Remarks on Geodesic and Curvature Preserving Mappings

M. Belger[1] and Klaus Beyer[2]

(1) Universität Leipzig, Germany
(2) Universität Leipzig, Germany

We ask for the converse of Gauss’ theorema egregium. Because in general isocurved manifolds are not isometric we ask stronger for isocurved, geodesic equivalent manifolds. For these we give a local criterion from which there follows that two-dimensional manifolds $\overline{\mathcal M}^2$ and of that type essentially are isometric, or both are Euclidean with an affine mapping in the ordinary sense.

Keywords: Curvature preserving mappings, geodesic mappings

Belger M., Beyer Klaus: Some Remarks on Geodesic and Curvature Preserving Mappings. Z. Anal. Anwend. 16 (1997), 73-81. doi: 10.4171/ZAA/750