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arXiv · 2605.15578

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

Shun Maeta·Miho Shito
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Abstract

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.

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Shun Maeta, Miho Shito. 2026-05-15. \lambda-biharmonic Riemannian submersions from manifolds with constant sectional curvature. https://arxiv.org/abs/2605.15578

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