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) |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
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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. |
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ISSN: | 1050-6926 1559-002X |
DOI: | 10.1007/s12220-024-01828-x |