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Prospects of differential geometry and its related fields - proceedings of the 3rd international colloquium on differential geometry and its related fields.

By: Adachi, ToshiakiMaterial type: TextTextPublication details: WSPC, 2013. Description: 1 online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 1306120349; 9781306120340; 9789814541817; 9814541818Subject(s): Geometry, Differential | MATHEMATICS -- Essays | MATHEMATICS -- Pre-Calculus | MATHEMATICS -- Reference | Geometry, DifferentialGenre/Form: Electronic books. | Electronic books. Additional physical formats: Print version:: No titleDDC classification: 510 | 516.36 LOC classification: QA3Online resources: Click here to access online
Contents:
Preface; Organizing and Scientific Advisory Committees; Presentations; CONTENTS; Geometry of biharmonic maps: L2-rigidity, biharmonic Lagrangian submanifolds of Kahler manifolds, and conformal change of metrics Hajime URAKAWA; 1. Introduction and the generalized Chen's conjecture; 2. L2-rigidity theorem of biharmonic maps; 3. Lagrangian submanifolds of Kahler manifolds; 4. Conformal change of metrics and biharmonic maps; Bibliography; Homogeneous Einstein metrics on generalized flag manifolds with G2-type t-roots Andreas ARVANITOYEORGOS, Ioannis CHRYSIKOS and Yusuke SAKANE; 1. Introduction.
2. Ricci tensor of a compact homogeneous space G/K3. Riemannian submersion; 4. Decomposition associated to generalized flag manifolds; 5. The classification of generalized flag manifolds with G2-type t-roots; 6. Kahler Einstein metrics of a generalized flag manifold; 7. Generalized flag manifolds with two or three isotropy summands; 8. Generalized flag manifolds with G2-type t-roots; 9. Proof of the theorems; Acknowledgments; Bibliography; Applications of the Gaussian integers in coding theory Stefka BOUYUKLIEVA; 1. Introduction; 2. Some properties of the Gaussian integers.
3. Constellations and distances4. OMEC codes; 5. Codes correcting errors of Mannheim weight ≥ 2; Bibliography; A survey on generalized Liouville manifolds Midori GOTO; 1. Introduction; 2. Elliptic Coordinates; 3. Liouville Surfaces; 4. Definitions of Generalized Liouville Manifolds; 5. Lorentz-Liouville Surfaces; 6. Quadratic Surfaces in R3; 7. Further Results; Bibliography; The relativistic non-linear quantum dynamics from the CPN−1 geometry Peter LEIFER; 1. Introduction; 2. Intrinsic unification of relativity and quantum principles; 3. Affine non-Abelian gauge potential.
4. Dynamical spacetime5. Self-interacting quantum electron; 6. Solutions of the "field-shell" quasi-linear PDE's; 7. State-dependent Jacobi gauge fields; 8. Conclusion and future outlook; Acknowledgements; Bibliography; Wave equations, integral transforms, and twistor theory on indefinite geometry Fuminori NAKATA; 1. Introduction; 2. Small circles on the 2-sphere; 3. Circles on the cylinder; 4. General method on the twistor correspondence; 4.1. Partial indices of a holomorphic disk; 4.2. Construction of (−−++) self-dual space; 4.3. Construction of (−++) Einstein-Weyl structure.
5. Twistor theory for Tod-Kamada metric5.1. Model case; 5.2. Tod-Kamada metric; 5.3. Twistor space of Tod-Kamada metric; 6. Twsitor theory for indefinite self-dual metric on R4; 6.1. Model case; 6.2. Deformation of the twistor correspondence; Bibliography; A dynamical systematic aspect of horocyclic circles in a complex hyperbolic space Toshiaki ADACHI; 1. Introduction; 2. Circles on a complex space form; 3. Sasakian magnetic fields; 4. Extrinsic circular trajectories; 5. Other trajectories for Sasakian magnetic fields; Bibliography.
Summary: This volume consists of contributions by the main participants of the 3rd International Colloquium on Differential Geometry and its Related Fields (ICDG2012), which was held in Veliko Tarnovo, Bulgaria. Readers will find original papers by specialists and well-organized reports of recent developments in the fields of differential geometry, complex analysis, information geometry, mathematical physics and coding theory. This volume provides significant information that will be useful to researchers and serves as a good guide for young scientists. It is also for those who wish to start investigat.
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This volume consists of contributions by the main participants of the 3rd International Colloquium on Differential Geometry and its Related Fields (ICDG2012), which was held in Veliko Tarnovo, Bulgaria. Readers will find original papers by specialists and well-organized reports of recent developments in the fields of differential geometry, complex analysis, information geometry, mathematical physics and coding theory. This volume provides significant information that will be useful to researchers and serves as a good guide for young scientists. It is also for those who wish to start investigat.

Print version record.

Preface; Organizing and Scientific Advisory Committees; Presentations; CONTENTS; Geometry of biharmonic maps: L2-rigidity, biharmonic Lagrangian submanifolds of Kahler manifolds, and conformal change of metrics Hajime URAKAWA; 1. Introduction and the generalized Chen's conjecture; 2. L2-rigidity theorem of biharmonic maps; 3. Lagrangian submanifolds of Kahler manifolds; 4. Conformal change of metrics and biharmonic maps; Bibliography; Homogeneous Einstein metrics on generalized flag manifolds with G2-type t-roots Andreas ARVANITOYEORGOS, Ioannis CHRYSIKOS and Yusuke SAKANE; 1. Introduction.

2. Ricci tensor of a compact homogeneous space G/K3. Riemannian submersion; 4. Decomposition associated to generalized flag manifolds; 5. The classification of generalized flag manifolds with G2-type t-roots; 6. Kahler Einstein metrics of a generalized flag manifold; 7. Generalized flag manifolds with two or three isotropy summands; 8. Generalized flag manifolds with G2-type t-roots; 9. Proof of the theorems; Acknowledgments; Bibliography; Applications of the Gaussian integers in coding theory Stefka BOUYUKLIEVA; 1. Introduction; 2. Some properties of the Gaussian integers.

3. Constellations and distances4. OMEC codes; 5. Codes correcting errors of Mannheim weight ≥ 2; Bibliography; A survey on generalized Liouville manifolds Midori GOTO; 1. Introduction; 2. Elliptic Coordinates; 3. Liouville Surfaces; 4. Definitions of Generalized Liouville Manifolds; 5. Lorentz-Liouville Surfaces; 6. Quadratic Surfaces in R3; 7. Further Results; Bibliography; The relativistic non-linear quantum dynamics from the CPN−1 geometry Peter LEIFER; 1. Introduction; 2. Intrinsic unification of relativity and quantum principles; 3. Affine non-Abelian gauge potential.

4. Dynamical spacetime5. Self-interacting quantum electron; 6. Solutions of the "field-shell" quasi-linear PDE's; 7. State-dependent Jacobi gauge fields; 8. Conclusion and future outlook; Acknowledgements; Bibliography; Wave equations, integral transforms, and twistor theory on indefinite geometry Fuminori NAKATA; 1. Introduction; 2. Small circles on the 2-sphere; 3. Circles on the cylinder; 4. General method on the twistor correspondence; 4.1. Partial indices of a holomorphic disk; 4.2. Construction of (−−++) self-dual space; 4.3. Construction of (−++) Einstein-Weyl structure.

5. Twistor theory for Tod-Kamada metric5.1. Model case; 5.2. Tod-Kamada metric; 5.3. Twistor space of Tod-Kamada metric; 6. Twsitor theory for indefinite self-dual metric on R4; 6.1. Model case; 6.2. Deformation of the twistor correspondence; Bibliography; A dynamical systematic aspect of horocyclic circles in a complex hyperbolic space Toshiaki ADACHI; 1. Introduction; 2. Circles on a complex space form; 3. Sasakian magnetic fields; 4. Extrinsic circular trajectories; 5. Other trajectories for Sasakian magnetic fields; Bibliography.

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