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The Volume of Vector Fields on Riemannian Manifolds [[electronic resource] ] : Main Results and Open Problems / / by Olga Gil-Medrano
| The Volume of Vector Fields on Riemannian Manifolds [[electronic resource] ] : Main Results and Open Problems / / by Olga Gil-Medrano |
| Autore | Gil-Medrano Olga |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (131 pages) |
| Disciplina | 516 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Geometry
Mathematical analysis Geometry, Differential Global analysis (Mathematics) Manifolds (Mathematics) Analysis Differential Geometry Global Analysis and Analysis on Manifolds |
| ISBN | 3-031-36857-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Funding Acknowledgements -- Contents -- 1 Introduction -- 2 Minimal Sections of Tensor Bundles -- 2.1 Geometry of the Submanifold Determined by a Section of a Tensor Bundle -- 2.2 Minimal Sections of Tensor Bundles and Sphere Subbundles -- 2.3 First Variation of the Volume of Vector Fields: Minimal Vector Fields -- 2.4 Second Variation of the Volume of Vector Fields -- 2.5 The 2-Dimensional Case -- 2.6 Notes -- 2.6.1 Sections That Are Harmonic Maps -- 2.6.2 Sections That Are Critical Pointsof the Energy Functional -- 2.6.3 Minimal Oriented Distributions -- 3 Minimal Vector Fields of Constant Length on the Odd-Dimensional Spheres -- 3.1 Minimality of the Hopf Vector Fields -- 3.2 Study of the Stability of the Hopf Vector Fields -- 3.3 Stability of the Hopf Vector Fields of Odd-Dimensional Space Forms of Positive Curvature -- 3.4 Notes -- 3.4.1 Spheres and Their Quotients with Berger Metrics -- 3.4.2 The Minimality Condition for Unit Killing Vector Fields -- 3.4.3 Minimality of the Characteristic Vector Field of a Contact Riemannian Manifold -- 3.4.4 Minimal Invariant Vector Fields on Lie Groups and Homogeneous Spaces -- 3.4.5 Examples Related with Complex and Quaternionic Structures -- 4 Vector Fields of Constant Length of Minimum Volume on the Odd-Dimensional Spherical Space Forms -- 4.1 Hopf Vector Fields as Volume Minimisers in the 3-Dimensional Case -- 4.2 Hopf Vector Fields on 3-Dimensional Spheres with the Berger Metrics -- 4.3 Lower Bound of the Volume of Vector Fields of Constant Length -- 4.4 Asymptotic Behaviour of the Volume Functional -- 4.5 Notes -- 4.5.1 Unit Vector Fields on the Two-Dimensional Torus -- 4.5.2 Lower Bound of the Volume of Unit Vector Fields on Hypersurfaces of Rn+1 -- 4.5.3 Almost Hermitian Structures on S6 That Minimise the Volume -- 4.5.4 Minimisers of Functionals Related with the Energy.
5 Vector Fields of Constant Length on Punctured Spheres -- 5.1 The Radial Vector Fields -- 5.2 Parallel Transport Vector Fields -- 5.3 The Main Open Problem -- 5.4 Area Minimising Vector Fields on the 2-Sphere -- 5.5 Notes -- 5.5.1 Radial Vector Fields on Riemannian Manifolds -- 5.5.2 Minimisers of the Volume Among Unit Vector Fields with Singular Points -- References. |
| Record Nr. | UNINA-9910736012303321 |
Gil-Medrano Olga
|
||
| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The Volume of Vector Fields on Riemannian Manifolds [[electronic resource] ] : Main Results and Open Problems / / by Olga Gil-Medrano
| The Volume of Vector Fields on Riemannian Manifolds [[electronic resource] ] : Main Results and Open Problems / / by Olga Gil-Medrano |
| Autore | Gil-Medrano Olga |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (131 pages) |
| Disciplina | 516 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Geometry
Mathematical analysis Geometry, Differential Global analysis (Mathematics) Manifolds (Mathematics) Analysis Differential Geometry Global Analysis and Analysis on Manifolds |
| ISBN | 3-031-36857-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Funding Acknowledgements -- Contents -- 1 Introduction -- 2 Minimal Sections of Tensor Bundles -- 2.1 Geometry of the Submanifold Determined by a Section of a Tensor Bundle -- 2.2 Minimal Sections of Tensor Bundles and Sphere Subbundles -- 2.3 First Variation of the Volume of Vector Fields: Minimal Vector Fields -- 2.4 Second Variation of the Volume of Vector Fields -- 2.5 The 2-Dimensional Case -- 2.6 Notes -- 2.6.1 Sections That Are Harmonic Maps -- 2.6.2 Sections That Are Critical Pointsof the Energy Functional -- 2.6.3 Minimal Oriented Distributions -- 3 Minimal Vector Fields of Constant Length on the Odd-Dimensional Spheres -- 3.1 Minimality of the Hopf Vector Fields -- 3.2 Study of the Stability of the Hopf Vector Fields -- 3.3 Stability of the Hopf Vector Fields of Odd-Dimensional Space Forms of Positive Curvature -- 3.4 Notes -- 3.4.1 Spheres and Their Quotients with Berger Metrics -- 3.4.2 The Minimality Condition for Unit Killing Vector Fields -- 3.4.3 Minimality of the Characteristic Vector Field of a Contact Riemannian Manifold -- 3.4.4 Minimal Invariant Vector Fields on Lie Groups and Homogeneous Spaces -- 3.4.5 Examples Related with Complex and Quaternionic Structures -- 4 Vector Fields of Constant Length of Minimum Volume on the Odd-Dimensional Spherical Space Forms -- 4.1 Hopf Vector Fields as Volume Minimisers in the 3-Dimensional Case -- 4.2 Hopf Vector Fields on 3-Dimensional Spheres with the Berger Metrics -- 4.3 Lower Bound of the Volume of Vector Fields of Constant Length -- 4.4 Asymptotic Behaviour of the Volume Functional -- 4.5 Notes -- 4.5.1 Unit Vector Fields on the Two-Dimensional Torus -- 4.5.2 Lower Bound of the Volume of Unit Vector Fields on Hypersurfaces of Rn+1 -- 4.5.3 Almost Hermitian Structures on S6 That Minimise the Volume -- 4.5.4 Minimisers of Functionals Related with the Energy.
5 Vector Fields of Constant Length on Punctured Spheres -- 5.1 The Radial Vector Fields -- 5.2 Parallel Transport Vector Fields -- 5.3 The Main Open Problem -- 5.4 Area Minimising Vector Fields on the 2-Sphere -- 5.5 Notes -- 5.5.1 Radial Vector Fields on Riemannian Manifolds -- 5.5.2 Minimisers of the Volume Among Unit Vector Fields with Singular Points -- References. |
| Record Nr. | UNISA-996542671803316 |
|
Gil-Medrano Olga
|
||
| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
