Abstract:Let $(X, \Cal H)$ and $(X',\Cal H')$ be two strong biharmonic spaces in the sense of Smyrnelis whose associated harmonic spaces are Brelot spaces. A biharmonic morphism from $(X,\Cal H)$ to $(X',\Cal H')$ is a continuous map from $X$ to $X'$ which preserves the biharmonic structures of $X$ and $X'$. In the present work we study this notion and characterize in some cases the biharmonic morphisms between $X$ and $X'$ in terms of harmonic morphisms between the harmonic spaces associated with $(X,\Cal H)$ and $(X',\Cal H')$ and the coupling kernels of them.
Keywords: harmonic space, harmonic morphism, biharmonic space, biharmonic function, biharmonic morphism
AMS Subject Classification: 31B30, 31C35, 31D05