Generalized self-dual bosonic membranes, vector cross-products and analyticity in higher dimensions

By generalizing the notion of self-duality for chiral currents and gauge fields to Nambu-Goto membranes, we exhibit a remarkable class of self-dual classical closed bosonic p-branes in n spacetime dimensions. The latter exist whenever a p-fold vector cross-product can be defined in Rn. Their connections to generalized Cauchy-Riemann analyticity, to exceptional geometries and supermembranes in critical dimensions 7 and 8 in particular are discussed. (orig.)