A short survey on biharmonic maps between Riemannian manifolds

Abstract

In this short survey we report on the theory of biharmonic maps between Riemannian manifolds.

20 pages

References in corpus (3)

• Explicit Formulas for Non-Geodesic Biharmonic Curves of the Heisenberg Group
• Biharmonic properties and conformal changes
• The Classification of Biharmonic Curves of Cartan-Vranceanu 3-Dimensional Spaces

Cited by in corpus (46)

• Constant mean curvature and totally umbilical biharmonic surfaces in 3-dimensional geometries
• Weakly convex biharmonic hypersurfaces in nonpositive curvature space forms are minimal
• Biharmonic maps from a 2-sphere
• Classifications and Isolation Phenomena of Bi-Harmonic Maps and Bi-Yang-Mills Fields
• Unique continuation theorems for biharmonic maps
• On the generalized Chen's conjecture on biharmonic submanifolds
• A Liouville-type theorem for biharmonic maps between complete Riemannian manifolds with small energies
• Biharmonic maps into Sol and Nil spaces
• Polyharmonic maps into the Euclidean space
• Biharmonic hypersurfaces with constant scalar curvature in space forms
• Reduction methods for the bienergy
• Biharmonic space-like hypersurfaces in pseudo-Riemannian space
• The stress-energy tensor for biharmonic maps
• New Examples of Biharmonic Submanifolds in $C{P}^n$ and $S^{2n+1}$
• On the geometry of biharmonic submanifolds in Sasakian space forms
• Biharmonic hypersurfaces in Riemannian manifolds
• Sasaki manifolds, Kaehler cone manifolds and biharmonic submanifolds
• Biharmonic curves into quadrics
• Biharmonic surfaces of ${\mathbb{S}}^4$
• On conformal biharmonic immersions
• Explicit formulas for biharmonic submanifolds in Sasakian space forms
• Explicit formulas for biharmonic submanifolds in non-Euclidean 3-spheres
• f-Biharmonic and bi-f-harmonic submanifolds of generalized space forms
• Biharmonic submanifolds into ellipsoids
• Biharmonic maps from tori into a 2-sphere
• Biharmonic homogeneous hypersurfaces in compact symmetric spaces
• Conformal change of Riemannian metrics and biharmonic maps
• The biharmonicity of sections of the tangent bundle
• On harmonic and biharmonic maps from gradient Ricci solitons
• Nonexistence of proper $p$-biharmonic maps and Liouville type theorems I: case of $p\ge 2$
• New examples of r-harmonic immersions into the sphere
• Triharmonic isometric immersions into a manifold of non-positively constant curvature
• Submanifolds with Biharmonic Gauss Map
• On the stability of the equator map for higher order energy functionals
• Les applications conforme-harmoniques
• Biharmonic maps in two dimensions
• The biharmonic stress-energy tensor and the Gauss map
• A note on biharmonic curves in Sasakian space forms
• On the Gauss Map with Vanishing Biharmonic stress-energy tensor
• Removable singularities and bubbling of harmonic maps and biharmonic maps
• Biharmonic integral $\mathcal{C}$-parallel submanifolds in 7-dimensional Sasakian space forms
• Quasi-biharmonic Lagrangian surfaces in Lorentzian complex space forms
• Harmonic maps and biharmonic Riemanian submersions
• Harmonic morphisms of Allof-Wallach spaces of positive curvature
• Biharmonic Hermitian vector bundles over compact Kaehlar Einstein manifolds
• Biharmonic constant mean curvature surfaces in Killing submersions