Abstract
For every transnormal m-manifold V (see [3] or [7]) in ℝn ν:V→W, mapping pεV into its normal plane ν(p) is a covering map onto a submanifold W of the open Grassmannian Hn,n−m of all (n−m)-dimensional planes in ℝn. The transnormal frame T:=ν−1(ν(p)) admits a transitive operation by a group J of isometries. The group action of the covering transformations of (V,ν,W) on T commutes with the action of J. The elements of J, which are restrictions of covering transformations to T, are exactly the elements of the centre of J. This property is applied to show the existence of nontrivial covering transformations of (V,ν,W) for n−m≦3.
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Diese Arbeit faßt die Kapitel 5, 6 und 7 der von der Fakultät für Allgemeine Ingenieurwissenschaften der TU Berlin genehmigten Dissertation [6] zusammen.
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Wegner, B. Decktransformationen transnormaler Mannigfaltigkeiten. Manuscripta Math 4, 179–199 (1971). https://doi.org/10.1007/BF01169411
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DOI: https://doi.org/10.1007/BF01169411