A Bernstein Theorem for Minimal Maps with Small Second Fundamental Form

Felix Lubbe

doi:10.1007/s00025-018-0923-5

paper

A Bernstein Theorem for Minimal Maps with Small Second Fundamental Form

arXiv:1711.09878 · doi:10.1007/s00025-018-0923-5

Abstract

We consider minimal maps $f : M \to N$ between Riemannian manifolds $(M, g_{M})$ and $(N, g_{N})$ , where $M$ is compact and where the sectional curvatures satisfy $sec_{N} \leq σ \leq sec_{M}$ for some $σ > 0$ . Under certain assumptions on the differential of the map and the second fundamental form of the graph $Γ (f)$ of $f$ , we show that $f$ is either the constant map or a totally geodesic isometric immersion.

15 pages; comments are welcome!