In this paper we define a Moebius invariant metric and a Moebius invariant second fundamental form for submanifolds in ? n and show that in case of a hypersurface with n≥ 4 they determine the hypersurface up to Moebius transformations. Using these Moebius invariants we calculate the first variation of the moebius volume functional. We show that any minimal surface in ? n is also Moebius minimal and that the image in ? n of any minimal surface in ℝ n unter the inverse of a stereographic projection is also Moebius minimal. Finally we use the relations between Moebius invariants to classify all surfaces in ?3 with vanishing Moebius form.
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