Minimal isometric immersions into $S^2$ x $R$ and $H^2$ x $R$

Benoit Daniel (1)

1 IECL - Institut Élie Cartan de Lorraine

For a given simply connected Riemannian surface Σ, we relate the problem of finding minimal isometric immersions of Σ into S 2 × R or H 2 × R to a system of two partial differential equations on Σ. We prove that a constant intrinsic curvature minimal surface in S 2 ×R or H 2 ×R is either totally geodesic or part of an associate surface of a certain limit of catenoids in H 2 ×R. We also prove that if a non constant curvature Riemannian surface admits a continuous one-parameter family of minimal isometric immersions into S 2 × R or H 2 × R, then all these immersions are associate.

Domaines: Mathématiques [math]

Benoit Daniel. Minimal isometric immersions into $S^2$ x $R$ and $H^2$ x $R$. Indiana University Mathematics Journal, 2015, 64 (5), pp.1425-1445. ⟨hal-01097511⟩