\lambda-biharmonic Riemannian submersions from manifolds with constant sectional curvature

In this paper, we study \lambda-biharmonic Riemannian submersions, which generalize biharmonic Riemannian submersions.

We prove nonexistence results for \lambda-biharmonic Riemannian submersions from (n + 1)-dimensional Riemannian manifolds with constant sectional curvature c to n-dimensional Riemannian manifolds.

Our results show that the critical value \lambda = 2(n - 1)c plays a decisive role.

We prove that if c \ge 0, or if c < 0 and \lambda \ne 2(n - 1)c, then any \lambda-biharmonic Riemannian submersion must be harmonic.

On the other hand, when \lambda = 2(n - 1)c with c < 0, we construct explicit examples of \lambda-biharmonic Riemannian submersions.