| Description |
1 online resource (xv, 167 pages) : illustrations |
| Contents |
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 |
| Summary |
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 equations and complex analysis. On the other hand, the relativity theory has led to the study of pseudo-Riemannian manifolds, which turns out to be the most general framework for the study of minimal submanifolds. However, most of the recent books on the subject still present the theory only in the Riemann |
| Bibliography |
Includes bibliographical references (pages 161-164) and index |
| Notes |
Print version record |
| Subject |
Riemannian manifolds.
|
|
Minimal submanifolds.
|
|
MATHEMATICS -- Geometry -- Analytic.
|
|
Minimal submanifolds
|
|
Riemannian manifolds
|
| Form |
Electronic book
|
| ISBN |
9789814291255 |
|
9814291250 |
|
