Tight immersions and local differential geometry

Details Tight immersions and local differential geometry Tight immersions and local differential geometry

1997-02-07

arxiv.org/abs/dg-ga/9702007v1

Mathematics

Differential Geometry

Plain TeX, 24 pages

Scientific paper

An immersion of a compact manifold is tight if it admits the minimal total absolute curvature over all immersions of the manifold. A prominent result in the study of minimal total absolute curvature immersions is the theorem of Chern and Lashof, which characterizes minimal total absolute curvature immersions, and tight immersions, of spheres into a Euclidean space. In this paper we examine tight immersions of highly connected manifolds; i.e., 2k-dimensional manifolds that are (k-1)-connected by not k-connected, and characterize the immersions of highest codimension.

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