Hypersurfaces of constant higher order mean curvature in M×R

We consider hypersurfaces of products M×R with constant r-th mean curvature — to be called Hr-hypersurfaces — where M is an arbitrary Riemannian manifold. We develop a general method for constructing them, and employ it to produce many examples for a variety of manifolds M, including all simply connected space forms and the Hadamard manifolds known as Damek-Ricci spaces. Uniqueness results for complete Hr-hypersurface of Hn×R or Sn×R (n≥3) are also obtained. This is a joint work with Ronaldo de Lima (UFRN) and Fernando Manfio (ICMC-USP).

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