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We relate centroaffine immersions to horizontal immersions g of Mⁿ into or . We also show that f is an equiaffine sphere, i.e. the centroaffine normal is a constant multiple of the Blaschke normal, if and only if g is minimal.
We introduce an inequality for graph hypersurfaces and prove a decomposition theorem in case equality holds.
We investigate pairs of surfaces in Euclidean 3-space with the same Weingarten operator in case that one surface is given as surface of revolution. Our local and global results complement global results on ovaloids of revolution from S-V-W-W.
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