Focal points and support functions in affine differential geometry |
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Authors: | Thomas E Cecil |
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Institution: | (1) Department of Mathematics, College of the Holy Cross, 01610 Worcester, MA, USA |
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Abstract: | The notions of focal point and support function are considered for a nondegenerate hypersurfaceM
n
in affine spaceR
n+1 equipped with an equiaffine transversal field. IfM
n
is locally strictly convex, these two concepts are related via an Index theorem concerning the critical points of the support functions onM
n
. This is used to obtain characterizations of spheres and ellipsoids in terms of the critical point behavior of certain classes of affine support functions.Research supported by NSF Grant No. DMS-9101961. |
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Keywords: | 53A15 53C40 |
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