Real and complex hedgehogs, their symplectic area, curvature and evolutes

Classical (real) hedgehogs can be regarded as the geometrical realiza-tions of formal di¤erences convex bodies in R n+1. Like bodies, identi…ed with their support functions. Adopting a pro-jective viewpoint, we prove that any holomorphic function h : C n ! 'support function' complex hedgehog H In same vein, introduce notion evolute such 2 , and natural (but apparently hitherto unknown) curvature, which allows us to interpret this locus centers curvature. It is course permissible think development 'Brunn-Minkowski theory for hedgehogs' (replacing Euclidean volumes by symplectic ones) might promising way research. We give …rst two results direction. next return real 2n endowed linear structure. study hedgehog. particularly focus our attention on 4 Kahler structure determined datum pure unit quaternion. parallel, area images oriented Hopf circles under parametrizations quaternionic curvature an image. Finally, consider brie ‡y convolution hedgehogs, particular case 4n hyperkahler vector space.