Biharmonic Riemannian submersions from 3-manifolds

DOI10.1007/s00209-010-0766-6zbMath1235.53065arXiv1002.4439OpenAlexW2020867324WikidataQ115388788 ScholiaQ115388788MaRDI QIDQ658328

Ye-Lin Ou, Ze-Ping Wang

Publication date: 12 January 2012

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.4439

zbMATH Keywords

Riemannian submersion3-manifoldbiharmonic mapharmonic morphism

Mathematics Subject Classification ID

Differential geometric aspects of harmonic maps (53C43) Harmonic maps, etc. (58E20)

Related Items (20)

Biharmonic maps from tori into a 2-sphere ⋮ Biharmonic maps from a 2-sphere ⋮ Biharmonic hypersurfaces with bounded mean curvature ⋮ Geometry of Sasaki manifolds, Kähler cone manifolds and bi-harmonic submanifolds ⋮ Biharmonic Riemannian submersions from a 3-dimensional BCV space ⋮ Biharmonic maps in two dimensions ⋮ Biharmonic holomorphic maps and conformally Kähler geometry ⋮ Biharmonic Riemannian submersions ⋮ Sasaki manifolds, Kähler cone manifolds and biharmonic submanifolds ⋮ Triharmonic isometric immersions into a manifold of non-positively constant curvature ⋮ Generalized harmonic morphisms and horizontally weakly conformal biharmonic maps ⋮ Biharmonic maps into a Riemannian manifold of non-positive curvature ⋮ Biharmonic maps from a complete Riemannian manifold into a non-positively curved manifold ⋮ Polyharmonic maps into the Euclidean space ⋮ Unnamed Item ⋮ Triharmonic Riemannian submersions from 3-dimensional space forms ⋮ Biharmonic maps on principal \(G\)-bundles over complete Riemannian manifolds of nonpositive Ricci curvature ⋮ Some recent work on biharmonic conformal maps ⋮ Biharmonic pseudo-Riemannian submersions from 3-manifolds ⋮ Harmonic maps and biharmonic Riemanian submersions

Cites Work

• Biharmonic submanifolds in spheres.
• Biharmonic maps and morphisms from conformal mappings
• Bernstein theorems for harmonic morphisms from \({\mathbb R}\) 3 and S 3
• A mapping of Riemannian manifolds which preserves harmonic functions
• Harmonic morphisms between Riemannian manifolds
• The fundamental equations of a submersion
• On the geometry of harmonic morphisms
• BIHARMONIC PSEUDO-RIEMANNIAN SUBMANIFOLDS IN PSEUDO-EUCLIDEAN SPACES
• Hypersurfaces in E⁴ with Harmonic Mean Curvature Vector Field
• A CLASSIFICATION OF HORIZONTALLY HOMOTHETIC SUBMERSIONS FROM SPACE FORMS OF NONNEGATIVE CURVATURE
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