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§31 Normals from a Point to a Manifold

Elsevier B.V.
DOI: 10.1016/s0079-8169(08)62015-2


Publisher Summary This chapter discusses normals from a point to a manifold. Let Mn be a regular compact C∞-manifold in Em with 0 < n < m. By definition of a focal point, the function fq is ND only if q is not a focal point of Mn. Let (q, ζ) be a straight arc orthogonal to Mn at a point ζ∈Mn . The term (q,ζ) an arc normal to Mn at ζ and assign this arc an index equal to the index of ζ as a critical point of fq. When m = n + 1 the chapter evaluates the index of a critical point ζ∈Mn of the distance function fq in terms of the centers of principal normal curvature of Mn on the normal to Mn at ζ.

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