Nonexistence results of minimal immersions (Q2504870)

The authors prove some non-existence results for minimal immersions of a manifold \(M\), of dimension at least \(3\) into a space with constant strictly negative curvature \(N\). In particular they show that if \(M\) admits a non zero parallel \(p\)-form, then \(M\) cannot be minimally immersed. When \(N\) is only a conformally flat manifold, the authors induce two functions on \(N\) using a natural number \(p\) and the smallest and greatest eigenvalue of the Ricci tensor. They then show that (1) if the signs of the above defined functions satisfy a certain condition and \(M\) admits a parallel \(p\)-form \(\alpha\), then there exists no \(\alpha\)-pluriharmonic immersion of \(M\) into \(N\), and (2) if the signs of the above defined functions satisfy another condition and \(M\) admits a parallel \(p\)-form \(\alpha\), then any isometric minimal immersion is always \(\alpha\)-pluriharmonic.