Abstract. Let M be a compact connected oriented n−1 dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from M to Rn. The results of , where mean curvature weighted metrics were studied, suggest incorporating Gauß curvature weights in the definition of the metric. This leads us to study metrics on shape space that are induced by metrics on the space of immersions of the form Gf (h, k) = Φ.¯g(h, k) vol(
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