N. H. Kuiper, "Minimal total absolute curvature for immersions", Invent. Math. 10 (1970), 209--238. Home/Search Document Not in Database Summary Related Articles Check |
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Polyhedral Metrics In Surface Reconstruction: Tight.. - Alboul, van Damme (1995) (2 citations) (Correct)
....For smooth manifolds immersed in an n dimensional Euclidean space R n ,there exist the notions of the Two Piece Property (T.P.P. introduced by Banchoff [Ban65, Ban70b] of the minimal total absolute curvature, defined by Chern and Lashof [CL57] and of tightness, defined by Kuiper [Kui70, Kui80]. These three notions are equivalent for closed surfaces in R 3 . Definition 5.2.1. A closed surface S in R 3 has minimal total absolute curvature if 1 2 Z S K dA = 4 #.S ; where K is the Gaussian curvature of S , dA is the area element of S, and #.S is the Euler characteristic of S ....
....absolute curvature, if we introduce a notion of absolute extrinsic curvature. The absolute extrinsic curvature is a PL analogue of absolute curvature, defined for differentiable manifolds. The definition of tightness can be reformulated in the terms of critical point theory (due to Kuiper) [Kui70]. As we deal with immersions now, we slightly change our notations, concerning the height functions, as introduced in section 3.3.6. Let f : M # R 3 an immersion of a smooth manifold into Euclidean three space. Let 6 denote the unit sphere in R 3 , for any unit vector # S n 1 the ....
N. H. Kuiper. Minimal total absolute curvature for immersions. Invent. math, 10:209--238, 1970.
Tight Submanifolds, Smooth and Polyhedral - Banchoff, Kühnel (1997) (Correct)
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N. H. Kuiper, "Minimal total absolute curvature for immersions", Invent. Math. 10 (1970), 209--238.
Polyhedral Metrics in Surface Reconstruction: Tight.. - Alboul, van Damme (1995) (2 citations) (Correct)
No context found.
N.H. Kuiper. Minimal total absolute curvature for immersions. Invent. math, 10:209--238, 1970.
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