Regular homotopy and total curvature II: sphere immersions into 3–space
نویسندگان
چکیده
منابع مشابه
Regular homotopy and total curvature I: circle immersions into surfaces
An immersion of manifolds is a map with everywhere injective differential. Two immersions are regularly homotopic if there exists a continuous 1–parameter family of immersions connecting one to the other. The Smale–Hirsch h–principle [8, 4] says that the space of immersions M → N , dim(M) < dim(N) is homotopy equivalent to the space of injective bundle maps TM → TN . In contrast to differential...
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We consider properties of the total absolute geodesic curvature functional on circle immersions into a Riemann surface. In particular, we study its behavior under regular homotopies, its infima in regular homotopy classes, and the homotopy types of spaces of its local minima. We also consider the total curvature functional on the space of 2-sphere immersions into 3-space in a similar spirit. We...
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We consider properties of the total absolute geodesic curvature functional on circle immersions into a Riemann surface. In particular, we study its behavior under regular homotopies, its infima in regular homotopy classes, and the homotopy types of spaces of its local minima. We also consider the total curvature functional on the space of 2-sphere immersions into 3-space in a similar spirit. We...
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1. Let M and M' denote complete riemannian manifolds of dimension n and m respectively, and suppose that M is compact and oriented. For simplicity we assume that both manifolds and their metrics are smooth (i.e. of class C). In terms of local co-ordinates (x, x, ...,x") on M and local co-ordinates (y,y, •••,/") on M', the riemannian metrics are written ds = gtJ dx l dx, ds' = g'aP dy* dy * wher...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2006
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2006.6.493