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We prove non-existence 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. When \\lambda \\ne 2(n - 1)c, we prove a nonexistence theorem, although a dimensional assumption is needed in the positive curvature case. On the other hand, when \\lambda = 2(n - 1)c, we prove a non-ex","authors_text":"Miho Shito, Shun Maeta","cross_cats":[],"headline":"λ-biharmonic Riemannian submersions from constant curvature manifolds do not exist except when curvature is negative and λ takes the critical value.","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-15T03:40:36Z","title":"\\lambda-biharmonic Riemannian submersions from manifolds with constant sectional curvature"},"references":{"count":38,"internal_anchors":1,"resolved_work":38,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"M. A. Akyol and Y.-L. Ou,Biharmonic Riemannian submersions, Ann. Mat. Pura Appl. (4)198(2019), no. 2, 559–570","work_id":"37296448-202f-4b8f-8280-70865984cbdd","year":2019},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"A. Balmu¸ s, S. Montaldo and C. Oniciuc,Classification results for biharmonic submanifolds in spheres, Israel J. Math.168(2008), 201–220","work_id":"f2a76bb5-fb49-48e2-b065-505561fc4ce4","year":2008},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"A. Balmu¸ s, S. Montaldo and C. Oniciuc,Biharmonic hypersurfaces in 4-dimensional space forms, Math. Nachr.283(2010), no. 12, 1696–1705","work_id":"0e2498f9-a000-4263-859b-a66fe335d0ae","year":2010},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"H. Bibi, E. Loubeau and C. Oniciuc,Unique continuation property for biharmonic hypersurfaces in spheres, Ann. Global Anal. Geom.60(2021), no. 4, 807–827","work_id":"903fbbb7-ac94-4268-9259-aef5c1207055","year":2021},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"R. Caddeo, S. Montaldo and C. Oniciuc,Biharmonic submanifolds ofS 3, Internat J. 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