Concepts from Tensor Analysis and Differential Geometry
- 1st Edition - January 1, 1961
- Imprint: Academic Press
- Author: Tracy Y. Thomas
- Editor: Richard Bellman
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 5 3 4 3 - 5
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 3 7 1 - 7
Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a s… Read more
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Request a sales quoteConcepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a skew-symmetric tensor and the curl of a vector in a coordinate manifold of three dimensions. It also explains Riemann spaces, affinely connected spaces, normal coordinates, and the general theory of extension. The book explores differential invariants, transformation groups, Euclidean metric space, and the Frenet formulae. The text describes curves in space, surfaces in space, mixed surfaces, space tensors, including the formulae of Gaus and Weingarten. It presents the equations of two scalars K and Q which can be defined over a regular surface S in a three dimensional Riemannian space R. In the equation, the scalar K, which is an intrinsic differential invariant of the surface S, is known as the total or Gaussian curvature and the scalar U is the mean curvature of the surface. The book also tackles families of parallel surfaces, developable surfaces, asymptotic lines, and orthogonal ennuples. The text is intended for a one-semester course for graduate students of pure mathematics, of applied mathematics covering subjects such as the theory of relativity, fluid mechanics, elasticity, and plasticity theory.
Preface1. Coordinate Manifolds2. Scalars3. Vectors and Tensors4. A Special Skew-Symmetric Tensor5. The Vector Product. Curl of a Vector6. Riemann Spaces7. Affinely Connected Spaces8. Normal Coordinates9. General Theory of Extension10. Absolute Differentiation11. Differential Invariants12. Transformation Groups13. Euclidean Metric Space14. Homogeneous and Isotropic Tensors15. Curves in Space. Frenet Formulae16. Surfaces in Space17. Mixed Surface and Space Tensors. Coordinate Extension and Absolute Differentiation18. Formulae of Gauss and Weingarten19. Gaussian and Mean Curvature of a Surface20. Equations of Gauss and Codazzi21. Principal Curvatures and Principal Directions22. Asymptotic Lines23. Orthogonal Ennuples and Normal Congruences24. Families of Parallel Surfaces25. Developable Surfaces. Minimal SurfacesGeneral ReferencesSubject Index
- Edition: 1
- Published: January 1, 1961
- No. of pages (eBook): 128
- Imprint: Academic Press
- Language: English
- Paperback ISBN: 9781483253435
- eBook ISBN: 9781483263717
RB
Richard Bellman
Affiliations and expertise
Departments of Mathematics,
Electrical Engineering, and Medicine
University of Southern California
Los Angeles, CaliforniaTT
Tracy Y. Thomas
Affiliations and expertise
Graduate Institute for Mathematics and Mechanics
Indiana University, Bloomington, Indiana