دانلود کتاب Introduction to Differential Geometry

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Preface\nContents\nCHAPTER I. CURVES IN SPACE\n 1. Curves and surfaces. The summation convention\n 2. Length of a curve. Linear element\n 3. Tangent to a curve. Order of contact. Osculating plane\n 4. Curvature. Principal normal. Circle of curvature\n 5. Binormal. Torsion\n 6. The Frenet formulas. The form of a curve in the neighborhood of a point\n 7. Intrinsic equations of a curve\n 8. Involutes and evolutes of a curve\n 9. The tangent surface of a curve. The polar surface. Osculating sphere\n 10. Parametric equations of a surface. Coordinates and coordinate curves in a surface\n 11. Tangent plane to a surface\n 12. Developable surfaces. Envelope of a one-parameter family of surfaces\nCHAPTER II. TRANSFORMATION OF COORDINATES. TENSOR CALCULUS\n 13. Transformation of coordinates. Curvilinear coordinates\n 14. The fundamental quadratic form of space\n 15. Contravariant vectors. Scalars\n 16. Length of a contravariant vector. Angle between two vectors\n 17. Covariant vectors. Contravariant and covariant components of a vector\n 18. Tensors. Symmetric and skew symmetric tensors\n 19. Addition, subtraction and multiplication of tensors. Contraction\n 20. The Christoffel symbols. The Riemann tensor\n 21. The Frenet formulas in general coordinates\n 22. Covariant differentiation\n 23. Systems of partial differential equations of the first order. Mixed systems\nCHAPTER III. INTRINSIC GEOMETRY OF A SURFACE\n 24. Linear element of a surface. First fundamental quadratic form of a surface. Vectors in a surface\n 25. Angle of two intersecting curves in a surface. Element of area\n 26. Families of curves in a surface. Principal directions\n 27. The intrinsic geometry of a surface. Isometric surfaces\n 28. The Christoffel symbols for a surface. The Riemannian curvature tensor. The Gaussian curvature of a surface\n 29. Differential parameters\n 30. Isometric orthogonal nets. Isometric coordinates\n 31. Isometric surfaces\n 32. Geodesies\n 33. Geodesic polar coordinates. Geodesic triangles\n 34. Geodesic curvature\n 35. The vector asociate to a given vector with respect to a curve. Parallelism of vectors\n 36. Conformal correspondence of two surfaces\n 37. Geodesiccorrespondenceoftwosurfaces\nCHAPTER IV. SURFACES IN SPACE\n 38. The second fundamental form of a surface\n 39. The equation of Gauss and the equations of Codazzi\n 40. Normal curvature of a surface. Principal radii of normal curvature\n 41. Lines of curvature of a surface\n 42. Conjugate directions and conjugate nets. Isometric-conjugate nets\n 43. Asymptotic directions and asymptotic lines. Mean conjugate directions. The Dupin indicatrix\n 44. Geodesic curvature and geodesic torsion of a curve\n 45. Parallel vectors in a surface\n 46. Spherical representation of a surface. The Gaussian curvature of a surface\n 47. Tangential coordinates of a surface\n 48. Surfaces of center of a surface. Parallel surfaces\n 49. Spherical and pseudospherical surfaces\n 50. Minimal surfaces\nBibliography\nIndex