Biharmonic and biconservative surfaces in Thurston geometries

 

We will explain first the notions of biharmonic and biconservative submanifolds in Riemannian manifolds. Then we will focus on surfaces with one of these properties in the eight 3-dimensional Thurston geometries (real space forms, product spaces, the Heisenberg group Nil, the solvmanifold Sol3, and the universal cover of PSL2(R)). We will present old and new results on their local and global geometry and will end with a recent  study of these surfaces in Sol3.