Geometry of Biharmonic Mappings

The author describes harmonic maps which are critical points of the energy functional, and biharmonic maps which are critical points of the bienergy functional. Also given are fundamental materials of the variational methods in differential geometry, and also fundamental materials of differential geometry.
Contents: Fundamental Materials on the Theory of Harmonic Maps and Biharmonic Maps:Fundamental Materials of Riemannian GeometryThe First and Second Variational Formulas of the EnergyRigidity and Abundance of Biharmonic Maps:Biharmonic Maps into a Riemannian Manifold of Non-positive CurvatureBiharmonic Submanifolds in a Riemannian Manifold with Non-positive CurvatureBiharmonic Hypersurfaces in a Riemannian Manifold with Non-positive Ricci CurvatureNote on Biharmonic Map EquationsHarmonic Maps into Compact Lie Groups and Integrable SystemsBiharmonic Maps into Symmetric Spaces and Integrable SystemsBubbling of Harmonic Maps and Biharmonic MapsConformal Change of Riemannian Metrics and Biharmonic MapsBiharmonic Submanifolds:Biharmonic Submanifolds in a Riemannian ManifoldSasaki Manifolds, Kähler Cone Manifolds and Biharmonic SubmanifoldsBiharmonic Lagrangian Submanifolds in Kähler ManifoldsFurther Developments on Biharmonic Maps:Rigidity of Transversally Biharmonic Maps between Foliated Riemannian ManifoldsCR-Rigidity of Pseudo Harmonic Maps and Pseudo Biharmonic MapsHarmonic Maps and Biharmonic Maps on the Principal Bundles and Warped Products
Readership: Researchers in global analysis, geometry, calculus of variations and partial differential equations. Harmonic Map;Biharmonic Map;Variational Method0Key Features:New theory and complete theory are described in detail