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arXiv · 2605.15578

λ-biharmonic Riemannian submersions from manifolds with constant sectional curvature

Shun Maeta·Miho Shito
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Abstract

In this paper, we study λ-biharmonic Riemannian submersions, which generalize biharmonic Riemannian submersions. We prove nonexistence results for λ-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 λ= 2(n - 1)c plays a decisive role. We prove that if c \ge 0, or if c < 0 and λ\ne 2(n - 1)c, then any λ-biharmonic Riemannian submersion must be harmonic. On the other hand, when λ= 2(n - 1)c with c < 0, we construct explicit examples of λ-biharmonic Riemannian submersions.

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Shun Maeta, Miho Shito. 2026-07-01. λ-biharmonic Riemannian submersions from manifolds with constant sectional curvature. https://arxiv.org/abs/2605.15578

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