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The \(^ 1C_ n^*\) spaces (a class of conformally-euclidean spaces) and their modeling in euclidean spaces. (Spanish) Zbl 0808.53009

The author considers a class of conformally pseudo-euclidean spaces, with dimension \(n\) and codimension 1, where the conformal scale factor is defined through a geometrical condition, namely a relation between the stright lines in the \((n + 1)\)-dimensional projective space and the conformal factors. Working mainly in dimensions \(n = 3\) and \(n = 4\), it is proven first that there exists a relation between the level surfaces of the conformal factor and the Ricci surfaces. These related surfaces belong to the same class, sharing the same curvature and other geometrical properties. Next, it is characterized the case when these surfaces are umbilic, by means of a very special geometrical property in the projective space. Finally, the conformal transformation groups are calculated for some of the representatives in the class.

MSC:

53A30 Conformal differential geometry (MSC2010)
53C20 Global Riemannian geometry, including pinching
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