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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, NJ :
World Scientific,
2011.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xv, 167 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 161-164) and index. |
| ISBN: | 9789814291255 9814291250 |
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| 505 | 0 | |a 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. | |
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| author | Anciaux, Henri |
| author_facet | Anciaux, Henri |
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| 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. |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-11-27T13:17:54Z |
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| isbn | 9789814291255 9814291250 |
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| spelling | Anciaux, Henri. Minimal submanifolds in pseudo-Riemannian geometry / Henri Anciaux. Singapore ; Hackensack, NJ : World Scientific, 2011. 1 online resource (xv, 167 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 161-164) and index. Print version record. 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. 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. Riemannian manifolds. http://id.loc.gov/authorities/subjects/sh85114045 Minimal submanifolds. http://id.loc.gov/authorities/subjects/sh85129486 Variétés de Riemann. Sous-variétés minimales. MATHEMATICS Geometry Analytic. bisacsh Minimal submanifolds fast Riemannian manifolds fast has work: Minimal submanifolds in pseudo-Riemannian geometry (Text) https://id.oclc.org/worldcat/entity/E39PCFG8m3wBDqfWWTgMXxQ4jd https://id.oclc.org/worldcat/ontology/hasWork Print version: Anciaux, Henri. Minimal submanifolds in pseudo-Riemannian geometry. Singapore ; Hackensack, NJ : World Scientific, 2011 9789814291248 (OCoLC)700137424 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=374884 Volltext |
| spellingShingle | Anciaux, Henri Minimal submanifolds in pseudo-Riemannian geometry / 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. Riemannian manifolds. http://id.loc.gov/authorities/subjects/sh85114045 Minimal submanifolds. http://id.loc.gov/authorities/subjects/sh85129486 Variétés de Riemann. Sous-variétés minimales. MATHEMATICS Geometry Analytic. bisacsh Minimal submanifolds fast Riemannian manifolds fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85114045 http://id.loc.gov/authorities/subjects/sh85129486 |
| title | Minimal submanifolds in pseudo-Riemannian geometry / |
| title_auth | Minimal submanifolds in pseudo-Riemannian geometry / |
| title_exact_search | Minimal submanifolds in pseudo-Riemannian geometry / |
| title_full | Minimal submanifolds in pseudo-Riemannian geometry / Henri Anciaux. |
| title_fullStr | Minimal submanifolds in pseudo-Riemannian geometry / Henri Anciaux. |
| title_full_unstemmed | Minimal submanifolds in pseudo-Riemannian geometry / Henri Anciaux. |
| title_short | Minimal submanifolds in pseudo-Riemannian geometry / |
| title_sort | minimal submanifolds in pseudo riemannian geometry |
| topic | Riemannian manifolds. http://id.loc.gov/authorities/subjects/sh85114045 Minimal submanifolds. http://id.loc.gov/authorities/subjects/sh85129486 Variétés de Riemann. Sous-variétés minimales. MATHEMATICS Geometry Analytic. bisacsh Minimal submanifolds fast Riemannian manifolds fast |
| topic_facet | Riemannian manifolds. Minimal submanifolds. Variétés de Riemann. Sous-variétés minimales. MATHEMATICS Geometry Analytic. Minimal submanifolds Riemannian manifolds |
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