Affine hypersurfaces admitting a pointwise symmetry
نویسندگان
چکیده
منابع مشابه
Indefinite affine hyperspheres admitting a pointwise symmetry
An affine hypersurface M is said to admit a pointwise symmetry, if there exists a subgroup G of Aut(T p M) for all p ∈ M , which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. Here, we consider 3-dimensional indefinite affine hyperspheres, i. e. S = HId (and thus S is trivially preserved). First we solve an algebraic problem. We determine the...
متن کاملIndefinite Affine Hyperspheres Admitting a Pointwise Symmetry . Part 2 ?
An affine hypersurface M is said to admit a pointwise symmetry, if there exists a subgroup G of Aut(TpM) for all p ∈ M , which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. Here, we consider 3-dimensional indefinite affine hyperspheres, i.e. S = HId (and thus S is trivially preserved). In Part 1 we found the possible symmetry groups G and ga...
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3-dimensional affine hypersurfaces admitting a pointwise SO(2)-or Z 3-symmetry Abstract In (equi-)affine differential geometry, the most important algebraic invariants are the affine (Blaschke) metric h, the affine shape operator S and the difference tensor K. A hypersurface is said to admit a point-wise symmetry if at every point there exists a linear transformation preserving the affine metri...
متن کاملHyperspheres Admitting a Pointwise Symmetry Part 1
An affine hypersurface M is said to admit a pointwise symmetry, if there exists a subgroup G of Aut(TpM) for all p ∈ M , which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. Here, we consider 3-dimensional indefinite affine hyperspheres, i. e. S = HId (and thus S is trivially preserved). First we solve an algebraic problem. We determine the n...
متن کاملInjections into Affine Hypersurfaces )
Let X be a smooth aane variety of dimension n > 2. Assume that the group H 1 (X; Z) is a torsion group and that (X) = 1. Let Y be a projectively smooth aane hypersurface Y C n+1 of degree d > 1, which is smooth at innnity. Then there is no injective polynomial mapping f : X ! Y: This contradicts a result of Peretz 5].
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ژورنال
عنوان ژورنال: Results in Mathematics
سال: 2005
ISSN: 0378-6218,1420-9012
DOI: 10.1007/bf03323369