Cargando…
Sub-Riemannian Geometry : General Theory and Examples.
A comprehensive text and reference on sub-Riemannian and Heisenberg manifolds using a novel and robust variational approach.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2009.
|
| Colección: | Encyclopedia of mathematics and its applications.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Mi 4500 | ||
|---|---|---|---|
| 001 | EBSCO_ocn850148893 | ||
| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
| 006 | m o d | ||
| 007 | cr |n||||||||| | ||
| 008 | 130625s2009 enk ob 001 0 eng d | ||
| 040 | |a EBLCP |b eng |e pn |c EBLCP |d OCLCQ |d OCLCO |d DEBSZ |d EUX |d OCLCO |d OCLCQ |d OCLCO |d OCLCF |d N$T |d CAMBR |d YDXCP |d IDEBK |d OCLCQ |d UAB |d OCLCQ |d AU@ |d UKAHL |d OCLCQ |d K6U |d INARC |d LUN |d MM9 |d OCLCQ |d OCLCO |d INTCL |d OCLCO |d OCLCQ |d OCLCO | ||
| 015 | |a GBA961067 |2 bnb | ||
| 019 | |a 843760933 |a 847526702 |a 1117882307 |a 1151344514 |a 1167481742 |a 1171150815 |a 1180938876 | ||
| 020 | |a 9781107096097 | ||
| 020 | |a 110709609X | ||
| 020 | |a 9781107089839 |q (electronic bk.) | ||
| 020 | |a 1107089832 |q (electronic bk.) | ||
| 020 | |a 9781139195966 |q (electronic bk.) | ||
| 020 | |a 1139195964 |q (electronic bk.) | ||
| 020 | |a 1107104149 |q (e-book) | ||
| 020 | |a 9781107104143 |q (e-book) | ||
| 020 | |z 9780521897303 | ||
| 020 | |z 0521897300 | ||
| 029 | 1 | |a DEBSZ |b 384344771 | |
| 029 | 1 | |a DKDLA |b 820120-katalog:9910052750005765 | |
| 035 | |a (OCoLC)850148893 |z (OCoLC)843760933 |z (OCoLC)847526702 |z (OCoLC)1117882307 |z (OCoLC)1151344514 |z (OCoLC)1167481742 |z (OCoLC)1171150815 |z (OCoLC)1180938876 | ||
| 050 | 4 | |a QA649 .C27 2009 | |
| 072 | 7 | |a MAT |x 012020 |2 bisacsh | |
| 082 | 0 | 4 | |a 516.3/73 |a 516.373 |
| 084 | |a 31.52 |2 bcl | ||
| 084 | |a SK 370 |2 rvk | ||
| 049 | |a UAMI | ||
| 100 | 1 | |a Calin, Ovidiu. | |
| 245 | 1 | 0 | |a Sub-Riemannian Geometry : |b General Theory and Examples. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2009. | ||
| 300 | |a 1 online resource (384 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Encyclopedia of Mathematics and its Applications ; |v v. 126 | |
| 505 | 0 | |a Cover; Half Title; Series Page; Title; Copyright; Dedication; Contents; Preface; Part I General Theory; 1 Introductory Chapter; 1.1 Differentiable Manifolds; 1.2 Submanifolds; 1.3 Distributions; 1.4 Integral Curves of a Vector Field; 1.5 Independent One-Forms; 1.6 Distributions Defined by One-Forms; 1.7 Integrability of One-Forms; 1.8 Elliptic Functions; 1.9 Exterior Differential Systems; 1.10 Formulas Involving Lie Derivative; 1.11 Pfaff Systems; 1.12 Characteristic Vector Fields; 1.13 Lagrange-Charpit Method; 1.14 Eiconal Equation on the Euclidean Space; 1.15 Hamilton-Jacobi Equation on Rn. | |
| 505 | 8 | |a 2 Basic Properties2.1 Sub-Riemannian Manifolds; 2.2 The Existence of Sub-Riemannian Metrics; 2.3 Systems of Orthonormal Vector Fields at a Point; 2.4 Bracket-Generating Distributions; 2.5 Non-Bracket-Generating Distributions; 2.6 Cyclic Bracket Structures; 2.7 Strong Bracket-Generating Condition; 2.8 Nilpotent Distributions; 2.9 The Horizontal Gradient; 2.10 The Intrinsic and Extrinsic Ideals; 2.11 The Induced Connection and Curvature Forms; 2.12 The Iterated Extrinsic Ideals; 3 Horizontal Connectivity; 3.1 Teleman's Theorem; 3.2 Carathéodory's Theorem; 3.3 Thermodynamical Interpretation. | |
| 505 | 8 | |a 3.4 A Global Nonconnectivity Example3.5 Chow's Theorem; 4 The Hamilton-Jacobi Theory; 4.1 The Hamilton-Jacobi Equation; 4.2 Length-Minimizing Horizontal Curves; 4.3 An Example: The Heisenberg Distribution; 4.4 Sub-Riemannian Eiconal Equation; 4.5 Solving the Hamilton-Jacobi Equation; 5 The Hamiltonian Formalism; 5.1 The Hamiltonian Function; 5.2 Normal Geodesics and Their Properties; 5.3 The Nonholonomic Constraint; 5.4 The Covariant Sub-Riemannian Metric; 5.5 Covariant and Contravariant Sub-Riemannian Metrics; 5.6 The Acceleration Along a Horizontal Curve. | |
| 505 | 8 | |a 5.7 Horizontal and Cartesian Components5.8 Normal Geodesics as Length-Minimizing Curves; 5.9 Eigenvectors of the Contravariant Metric; 5.10 Poisson Formalism; 5.11 Invariants of a Distribution; 6 Lagrangian Formalism; 6.1 Lagrange Multipliers; 6.2 Singular Minimizers; 6.3 Regular Implies Normal; 6.4 The Euler-Lagrange Equations; 7 Connections on Sub-Riemannian Manifolds; 7.1 The Horizontal Connection; 7.2 The Torsion of the Horizontal Connection; 7.3 Horizontal Divergence; 7.4 Connections on Sub-Riemannian Manifolds; 7.5 Parallel Transport Along Horizontal Curves. | |
| 505 | 8 | |a 7.6 The Curvature of a Connection7.7 The Induced Curvature; 7.8 The Metrical Connection; 7.9 The Flat Connection; 8 Gauss' Theory of Sub-Riemannian Manifolds; 8.1 The Second Fundamental Form; 8.2 The Adapted Connection; 8.3 The Adapted Weingarten Map; 8.4 The Variational Problem; 8.5 The Case of the Sphere S3; Part II Examples and Applications; 9 Heisenberg Manifolds; 9.1 The Quantum Origins of the Heisenberg Group; 9.2 Basic Definitions and Properties; 9.3 Determinants of Skew-Symmetric Matrices; 9.4 Heisenberg Manifolds as Contact Manifolds; 9.5 The Curvature Two-Form. | |
| 500 | |a 9.6 Volume Element on Heisenberg Manifolds. | ||
| 520 | |a A comprehensive text and reference on sub-Riemannian and Heisenberg manifolds using a novel and robust variational approach. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references (pages 363-366) and index. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Geodesics (Mathematics) | |
| 650 | 0 | |a Geometry, Riemannian. | |
| 650 | 0 | |a Riemannian manifolds. | |
| 650 | 0 | |a Submanifolds. | |
| 650 | 6 | |a Géodésiques (Mathématiques) | |
| 650 | 6 | |a Géométrie de Riemann. | |
| 650 | 6 | |a Variétés de Riemann. | |
| 650 | 6 | |a Sous-variétés (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Analytic. |2 bisacsh | |
| 650 | 7 | |a Geodesics (Mathematics) |2 fast | |
| 650 | 7 | |a Geometry, Riemannian |2 fast | |
| 650 | 7 | |a Riemannian manifolds |2 fast | |
| 650 | 7 | |a Submanifolds |2 fast | |
| 700 | 1 | |a Chang, Der-Chen. | |
| 776 | 0 | 8 | |i Print version: |a Calin, Ovidiu. |t Sub-Riemannian Geometry : General Theory and Examples. |d Cambridge : Cambridge University Press, ©2009 |z 9780521897303 |
| 830 | 0 | |a Encyclopedia of mathematics and its applications. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569394 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH25052676 | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH37561664 | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH26385551 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL1178995 | ||
| 938 | |a EBSCOhost |b EBSC |n 569394 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis25780872 | ||
| 938 | |a Internet Archive |b INAR |n subriemanniangeo0000cali | ||
| 938 | |a YBP Library Services |b YANK |n 10705854 | ||
| 938 | |a YBP Library Services |b YANK |n 10759680 | ||
| 938 | |a YBP Library Services |b YANK |n 10760959 | ||
| 938 | |a YBP Library Services |b YANK |n 10794867 | ||
| 994 | |a 92 |b IZTAP | ||