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I include this as a little illustration of my former work -- enjoy!
“Invariants of Conformal and Projective Structures.”
By Christian Steglich, 1995.
Results in Mathematics 27, 188-193.
While in Euclidean, equiaffine or centroaffine differential geometry,
there exists a unique, distinguished normalization of a regular hypersurface immersion x : Mn → An+1,
in the geometry of the general affine transformation group, there
only exists a distinguished class of such normalizations: the
class of relative normalizations. Thus, the appropriate invariants
for speaking about affine hypersurfaces are invariants of the induced classes, e.g.
the conformal class of induced metrics and the projective class of induced conormal
connections.
The aim of this paper is to study such invariants. As an application,
we reformulate the fundamental theorem of affine differential geometry.
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(166 KB)
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