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Geometry of Vector Fields [Kõva köide]

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(Inst. of Low Temperature Physics & Eng. Kharkov, Ukraine)
  • Formaat: Hardback, 210 pages, kõrgus x laius: 254x178 mm, kaal: 544 g
  • Ilmumisaeg: 23-Feb-2000
  • Kirjastus: Taylor & Francis Ltd
  • ISBN-10: 9056992015
  • ISBN-13: 9789056992019
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Geometry of Vector FieldsSuurem pilt
  • Formaat: Hardback, 210 pages, kõrgus x laius: 254x178 mm, kaal: 544 g
  • Ilmumisaeg: 23-Feb-2000
  • Kirjastus: Taylor & Francis Ltd
  • ISBN-10: 9056992015
  • ISBN-13: 9789056992019
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9789056992019.html
Märksõnad:
A specialist in classical differential geometry, Aminov (Ukrainian Academy of Sciences, Kharkov) presents a classical approach to the foundations and development of the geometry of vector fields, describing vector fields in three-dimensional Euclidean space and triply-orthogonal systems. He also discusses Pfaffian forms and systems in n -dimensional space, foliations and their Godbillon-Vey invariant, and applications in mechanics. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Presenting a classical approach to the foundations and development of the geometry of vector fields, this volume space, three orthogonal systems, and applications in mechanics. Other topics, including vector fields, Pfaff forms and systems in n-dimensional space, foliations and Godbillon-Vey invariant, are also considered. There is much interest in the study of geometrical objects in n-dimensional Euclidean space, and this volume provides a useful and comprehensive presentation.
Preface xi
Vector Fields in Three-Dimensional Euclidean Space
1(98)
The Non-Holonomicity Value of a Vector Field
1(7)
Normal Curvature of a Vector Field and Principal Normal Curvatures of the First Kind
8(4)
The Streamline of Vector Field
12(2)
The Straightest and the Shortest Lines
14(8)
The Total Curvature of the Second Kind
22(7)
The Asymptotic Lines
29(3)
The First Divergent Form of Total Curvature of the Second Kind
32(2)
The Second Divergent Representation of Total Curvature of the Second Kind
34(3)
The Interrelation of Two Divergent Representations of the Total Curvatures of the Second Kind
37(2)
The Generalization of the Gauss-Bonnet Formula for the Closed Surface
39(3)
The Gauss-Bonnet Formula for the Case of a Surface with a Boundary
42(7)
The Extremal Values of Geodesic Torsion
49(3)
The Singularities as the Sources of Curvature of a Vector Field
52(3)
The Mutual Restriction of the Fundamental Invariants of a Vector Field and the Size of Domain of Definition
55(5)
The Behavior of Vector Field Streamlines in a Neighborhood of a Closed Streamline
60(6)
The Complex Non-Holonomicity
66(3)
The Analogues of Gauss-Weingarten Decompositions and the Bonnet Theorem Analogue
69(2)
Triorthogonal Family of Surfaces
71(8)
Triorthogonal Bianchi System
79(3)
Geometrical Properties of the Velocity Field of an Ideal Incompressible Liquid
82(5)
The Caratheodory-Rashevski Theorem
87(5)
Parallel Transport on the Non-Holonomic Manifold and the Vagner Vector
92(7)
Vector Fields and Differential Forms in Many-Dimensional Euclidean and Riemannian Spaces
99(64)
The Unit Vector Field in Many-Dimensional Euclidean Space
99(2)
The Regular Vector Field Defined in a Whole Space
101(3)
The Many-Dimensional Generalization of the Gauss-Bonnet Formula to the Case of a Vector Field
104(5)
The Family of Parallel Hypersurfaces of Riemannian Space
109(2)
The Constant Vector Fields and the Killing Fields
111(3)
On Symmetric Polynomials of Principal Curvatures of a Vector Field on Riemannian Space
114(2)
The System of Pfaff Equations
116(7)
An Example from the Mechanics of Non-Holonomic Constraints
123(1)
The Exterior Differential Forms
124(5)
The Exterior Codifferential
129(2)
Some Formulas for the Exterior Differential
131(2)
Simplex, the Simplex Orientation and the Induced Orientation of a Simplex Boundary
133(1)
The Simplicial Complex, the Incidence Coefficients
134(1)
The Integration of Exterior Forms
135(4)
Homology and Cohomology Groups
139(2)
Foliations on the Manifolds and the Reeb's Example
141(2)
The Godbillon-Vey Invariant for the Foliation on a Manifold
143(4)
The Expression for the Hopf Invariant in Terms of the Integral of the Field Non-Holonomicity Value
147(3)
Vector Fields Tangent to Spheres
150(9)
On the Family of Surfaces which Fills a Ball
159(4)
References 163(6)
Subject Index 169(2)
Author Index 171