Informationen zum Autor VLADIMIR BALAN, PhD, is Professor in the Department of Mathematics and Informatics at the University Politehnica of Bucharest, Romania. He has published extensively in his areas of research interest, which include harmonic maps, variational problems in fiber bundles, and generalized gauge theory and its applications in mechanics and mathematical physics. MIRCEA NEAGU, PhD, is Assistant Professor in the Department of Algebra, Geometry, and Differential Equations at the Transilvania University of Brä ov, Romania. He is the author of more than thirty-five journal articles on jet Riemann-Lagrange geometry and its applications. Klappentext Develops the theory of jet single-time Lagrange geometry and presents modern-day applicationsJet Single-Time Lagrange Geometry and Its Applications guides readers through the advantages of jet single-time Lagrange geometry for geometrical modeling. With comprehensive chapters that outline topics ranging in complexity from basic to advanced, the book explores current and emerging applications across a broad range of fields, including mathematics, theoretical and atmospheric physics, economics, and theoretical biology.The authors begin by presenting basic theoretical concepts that serve as the foundation for understanding how and why the discussed theory works. Subusequent chapters compare the geometrical and physical aspects of jet relativistic time-dependent Lagrange geometry to the classical time-dependent Lagrange geometry. A collection of jet geometrical objects are also examined such as d-tensors, relativistic time-dependent semisprays, harmonic curves, and nonlinear connections. Numerous applications, including the gravitational theory developed by both the Berwald-Moór metric and the Chernov metric, are also presented.Throughout the book, the authors offer numerous examples that illustrate how the theory is put into practice, and they also present numerous applications in which the solutions of first-order ordinary differential equation systems are regarded as harmonic curves on 1-jet spaces. In addition, numerous opportunities are provided for readers to gain skill in applying jet single-time Lagrange geometry to solve a wide range of problems.Extensively classroom-tested to ensure an accessible presentation, Jet Single-Time Lagrange Geometry and Its Applications is an excellent book for courses on differential geometry, relativity theory, and mathematical models at the graduate level. The book also serves as an excellent reference for researchers, professionals, and academics in physics, biology, mathematics, and economics who would like to learn more about model-providing geometric structures. Zusammenfassung Develops the theory of jet single-time Lagrange geometry and presents modern-day applications Jet Single-Time Lagrange Geometry and Its Applications guides readers through the advantages of jet single-time Lagrange geometry for geometrical modeling. Inhaltsverzeichnis Preface. Part I. The Jet Single-Time Lagrange Geometry 1. Jet geometrical objects depending on a relativistic time 3 1.1 d-Tensors on the 1-jet space J1(R, M) 4 1.2 Relativistic time-dependent semisprays. Harmonic curves 6 1.3 Jet nonlinear connection. Adapted bases 11 1.4 Relativistic time-dependent and jet nonlinear connections 16 2. Deflection d-tensor identities in the relativistic time-dependent Lagrange geometry 19 2.1 The adapted components of jet -linear connections 19 2.2 Local torsion and curvature d-tensors 24 2.3 Local Ricci identities and nonmetrical deflection d-tensors 30 3. Local Bianchi identities in the relativistic time-dependent Lagrange geometry 33 3.1 The adapted components of h-normal -linear connections 33 3.2 Deflection d-tensor identities and local Bianchi identities for d-con...

Autorentext

VLADIMIR BALAN, PhD, is Professor in the Department of Mathematics and Informatics at the University Politehnica of Bucharest, Romania. He has published extensively in his areas of research interest, which include harmonic maps, variational problems in fiber bundles, and generalized gauge theory and its applications in mechanics and mathematical physics. MIRCEA NEAGU, PhD, is Assistant Professor in the Department of Algebra, Geometry, and Differential Equations at the Transilvania University of Brä ov, Romania. He is the author of more than thirty-five journal articles on jet Riemann-Lagrange geometry and its applications.

Klappentext

Develops the theory of jet single-time Lagrange geometry and presents modern-day applications Jet Single-Time Lagrange Geometry and Its Applications guides readers through the advantages of jet single-time Lagrange geometry for geometrical modeling. With comprehensive chapters that outline topics ranging in complexity from basic to advanced, the book explores current and emerging applications across a broad range of fields, including mathematics, theoretical and atmospheric physics, economics, and theoretical biology. The authors begin by presenting basic theoretical concepts that serve as the foundation for understanding how and why the discussed theory works. Subusequent chapters compare the geometrical and physical aspects of jet relativistic time-dependent Lagrange geometry to the classical time-dependent Lagrange geometry. A collection of jet geometrical objects are also examined such as d-tensors, relativistic time-dependent semisprays, harmonic curves, and nonlinear connections. Numerous applications, including the gravitational theory developed by both the Berwald-Moór metric and the Chernov metric, are also presented. Throughout the book, the authors offer numerous examples that illustrate how the theory is put into practice, and they also present numerous applications in which the solutions of first-order ordinary differential equation systems are regarded as harmonic curves on 1-jet spaces. In addition, numerous opportunities are provided for readers to gain skill in applying jet single-time Lagrange geometry to solve a wide range of problems. Extensively classroom-tested to ensure an accessible presentation, Jet Single-Time Lagrange Geometry and Its Applications is an excellent book for courses on differential geometry, relativity theory, and mathematical models at the graduate level. The book also serves as an excellent reference for researchers, professionals, and academics in physics, biology, mathematics, and economics who would like to learn more about model-providing geometric structures.

Inhalt

Preface. Part I. The Jet Single-Time Lagrange Geometry

1. Jet geometrical objects depending on a relativistic time 3

1.1 d-Tensors on the 1-jet space J1(R, M) 4

1.2 Relativistic time-dependent semisprays. Harmonic curves 6

1.3 Jet nonlinear connection. Adapted bases 11

1.4 Relativistic time-dependent and jet nonlinear connections 16

2. Deflection d-tensor identities in the relativistic time-dependent Lagrange geometry 19

2.1 The adapted components of jet -linear connections 19

2.2 Local torsion and curvature d-tensors 24

2.3 Local Ricci identities and nonmetrical deflection d-tensors 30

3. Local Bianchi identities in the relativistic time-dependent Lagrange geometry 33

3.1 The adapted components of h-normal -linear connections 33

3.2 Deflection d-tensor identities and local Bianchi identities for d-connections of Cartan type 37

4. The jet Riemann-Lagrange geometry of the relativistic time-dependent Lagrange spaces 43

4.1 Relativistic time-dependent Lagrange spaces 44

4.2 The canonical nonlinear connection 45

4.3 The Cartan canonical metrical linear connection 48

4.4 Relativistic time-dependent Lagrangian electromagnetism 50

4.5 Jet relativistic time-dependent Lagrangian gravitational theory 51

5. The jet single-time electrodynamics 57

5.1 Riemann-Lagrange geometry on the jet single-time Lagrange space of electrodynamics EDLn/1 58

5.2 Geometrical Maxwel…