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Minimal submanifolds in pseudo-Riemannian geometry /
Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space, the theory of minimal submanifolds have undergone considerable developments, involving techniques from related areas, such as the analysis of partial differential equatio...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, NJ :
World Scientific,
2011.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Submanifolds in pseudo-Riemannian geometry. 1.1. Pseudo-Riemannian manifolds. 1.2. Submanifolds. 1.3. The variation formulae for the volume. 1.4. Exercises
- 2. Minimal surfaces in pseudo-Euclidean space. 2.1. Intrinsic geometry of surfaces. 2.2. Graphs in Minkowski space. 2.3. The classification of ruled, minimal surfaces. 2.4. Weierstrass representation for minimal surfaces. 2.5. Exercises
- 3. Equivariant minimal hypersurfaces in space forms. 3.1. The pseudo-Riemannian space forms. 3.2. Equivariant minimal hypersurfaces in pseudo-Euclidean space. 3.3. Equivariant minimal hypersurfaces in pseudo-space forms. 3.4. Exercises
- 4. Pseudo-Kahler manifolds. 4.1. The complex pseudo-Euclidean space. 4.2. The general definition. 4.3. Complex space forms. 4.4. The tangent bundle of a pseudo-Kahler manifold. 4.5. Exercises
- 5. Complex and Lagrangian submanifolds in pseudo-Kahler manifolds. 5.1. Complex submanifolds. 5.2. Lagrangian submanifolds. 5.3. Minimal Lagrangian surfaces in C[symbol] with neutral metric. 5.4. Minimal Lagrangian submanifolds in C[symbol]. 5.5. Minimal Lagrangian submanifols in complex space forms. 5.6. Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface. 5.7. Exercises
- 6. Minimizing properties of minimal submanifolds. 6.1. Minimizing submanifolds and calibrations. 6.2. Non-minimizing submanifolds.