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A characterization of affine cylinders. (English) Zbl 0843.53012

Affine cylinders are characterized as the only hypersurfaces of type number 1 admitting non-flat locally symmetric connections. A class of non-metrizable locally symmetric connections on abstract manifolds is produced. The realization problem for locally symmetric connections of 1-codimensional nullity space is also discussed.

MSC:

53B25 Local submanifolds
53C05 Connections (general theory)
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References:

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