Biharmonic Riemannian Submersions from the Product Space M2×R

In this paper, we study biharmonic Riemannian submersions π : M 2 × R → ( N 2 , h ) from a product manifold onto a surface and obtain some local characterizations of such biharmonic maps. Our results show that when the target surface is flat, a proper biharmonic Riemannian submersion π : M 2 × R → (...

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Veröffentlicht in:The Journal of geometric analysis 2025, Vol.35 (1)
Hauptverfasser: Wang, Ze-Ping, Ou, Ye-Lin
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, we study biharmonic Riemannian submersions π : M 2 × R → ( N 2 , h ) from a product manifold onto a surface and obtain some local characterizations of such biharmonic maps. Our results show that when the target surface is flat, a proper biharmonic Riemannian submersion π : M 2 × R → ( N 2 , h ) is locally a projection of a special twisted product, and when the target surface is non-flat, π is locally a special map between two warped product spaces with a warping function that solves a single ODE. As a by-product, we also prove that there is a unique proper biharmonic Riemannian submersion H 2 × R → R 2 given by the projection of a warped product onto the Euclidean plane.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-024-01828-x