Abstract
Here we study the push-out space of a transnormal immersion of an m-dimensional compact manifold M without boundary into the Euclidean (m + k)-space and show that for an r-transnormal immersion with flat normal bundle, the push-out space has at most r components and this number can be attained in some cases, and any two components are isometric to each other.
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Kaya, Y. The push-out space of transnormal immersions. Arch. Math. 95, 283–292 (2010). https://doi.org/10.1007/s00013-010-0159-4
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DOI: https://doi.org/10.1007/s00013-010-0159-4