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  • Produktbild: Some Properties of Differentiable Varieties and Transformations
Band 13

Some Properties of Differentiable Varieties and Transformations With Special Reference to the Analytic and Algebraic Cases

Aus der Reihe Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge Band 13

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Beschreibung

Details

Einband

Taschenbuch

Erscheinungsdatum

11.11.2011

Verlag

Springer Berlin

Seitenzahl

198

Maße (L/B/H)

22,9/15,2/1,2 cm

Gewicht

321 g

Auflage

Second Edition 1971

Sprache

Englisch

ISBN

978-3-642-65008-6

Beschreibung

Details

Einband

Taschenbuch

Erscheinungsdatum

11.11.2011

Verlag

Springer Berlin

Seitenzahl

198

Maße (L/B/H)

22,9/15,2/1,2 cm

Gewicht

321 g

Auflage

Second Edition 1971

Sprache

Englisch

ISBN

978-3-642-65008-6

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

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Weitere Bände von Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

Weitere Bände von Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

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  • Produktbild: Some Properties of Differentiable Varieties and Transformations
  • Produktbild: Some Properties of Differentiable Varieties and Transformations
  • One. Differential Invariants of Point and Dual Transformations.-
    1. Local metrical study of point transformations.-
    2. Some topologico-differential invariants.-
    3. Projective construction of the above invariants.-
    4. Local metrical study of the dual transformations.-
    5. Calculation of the first order differential invariants just considered.-
    6. Some particular transformations. Relations between densities.-
    7. The curvature of hypersurfaces and of Pfaffian forms.- Historical Notes and Bibliography.- Two. Local Properties of Analytic Transformations at their United Points.-
    8. Coefficients of dilatation and residues of transformations in the analytic field.-
    9. Transfer to the Riemann variety.-
    10. Formal changes of coordinates.-
    11. Formal reduction to the canonical form for the arithmetically general transformations.-
    12. The case of arithmetically special transformations.-
    13. Criteria of convergence for the reduction procedure in the general case.-
    14. Iteration and permutability of analytic transformations.-
    15. On the united points of cyclic transformations.-
    16. Arithmetically general transformations not representable linearly.- Historical Notes and Bibliography.- Three. Invariants of Contact and of Osculation. The Concept of Cross-ratio in Differential Geometry.-
    17. Projective invariants of two curves having the same osculating spaces at a point.-
    18. A notable metric case.-
    19. An important extension.-
    20. Projective invariants of contact of differential elements of any dimension.-
    21. Two applications.-
    22. On certain varieties generated by quadrics.-
    23. The notion of cross-ratio on certain surfaces.-
    24. Applications to various branches of differential geometry.-
    25. Some extensions.- Historical Notes and Bibliography.- Four. Principal and Projective Curves of a Surface, and Some Applications.-
    26. Some results of projective-differential geometry.-
    27. The definition and main properties of the principal and projective curves.-
    28. Further properties of the above curves.-
    29. The use of the Laplace invariants and of the infinitesimal invariants.-
    30. Some classes of surfaces on which the concept of cross-ratio is particularly simple.-
    31. Point correspondences which conserve the projective curves.-
    32. Point correspondences which preserve the principal lines.-
    33. On the plane cone curves of a surface.- Historical Notes and Bibliography.- Five. Some Differential Properties in the Large of Algebraic Curves, their Intersections, and Self-correspondences.-
    34. The residues of correspondences on curves, and a topological invariant of intersection of two curves on a surface which contains two privileged pencils of curves.-
    35. A complement of the correspondence principle on algebraic curves.-
    36. A geometric characterization of Abelian integrals and their residues.-
    37. The first applications.-
    38. The equation of Jacobi, and some consequences.-
    39. The relation of Reiss, and some extensions.-
    40. Further algebro-differential properties.- Historical Notes and Bibliography.- Six. Extensions to Algebraic Varieties.-
    41. Generalizations of the equation of Jacobi.-
    42. Generalizations of the relation of Reiss.-
    43. The residue of an analytic transformation at a simple united point.-
    44. Some important particular cases.-
    45. Relations between residues at the same point.-
    46. The total residues of correspondences of valency zero on algebraic varieties.-
    47. The residues at isolated united points with arbitrary multiplicities.-
    48. Extensions to algebraic correspondences of arbitrary valency.-
    49. Applications to algebraic correspondences of a projective space into itself.- Historical Notes and Bibliography.- Seven. Veronese Varieties and Modules of Algebraic Forms.-
    50. n-regular points of differentiable varieties.-
    51. Some special properties of n-regular points of differentiable varieties.-
    52. On the freedom of hypersurfaces having assigned multiplicities at a set of points.-
    53. On the effective dimension of certain linear systems of hypersurfaces.-
    54. Two relations of Lasker concerning modules of hypersurfaces.-
    55. Some important criteria for a hypersurface to belong to a given module.-
    56. Some properties of the osculating spaces at the points of a Veronese variety Vd(n).-
    57. The ambients of certain subvarieties of Vd(n).-
    58. The isolated multiple intersections of d primals on Vd(n).-
    59. The regular multiple intersections on Vd(n).-
    60. A special property of the space associated with an isolated intersection on Vd(n) in the simple case.-
    61. On a theorem of Torelli and some complements.- Historical Notes and Bibliography.- Eight. Linear Partial Differential Equations.-
    62. Preliminary observations.-
    63. The reduction of differential equations to a canonical form.-
    64. Remarks on the solution of the differential equations.-
    65. The construction of the conditions of integrability.-
    66. The conditions of compatibility for a system of linear partial differential equations in one unknown.-
    67. The analytic case where the characteristic hypersurfaces intersect regularly.-
    68. An extension to the non-analytic case.-
    69. Some remarks on sets of linear partial differential equations in several unknowns.-
    70. The solution of a system of homogeneous equations.-
    71. The resolving system associated with a general set of m differential equations in m unknowns.- Historical Notes and Bibliography.- Nine. Projective Differential Geometry of Systems of Linear Partial Differential Equations.-
    72. r-osculating spaces to a variety.-
    73. Surfaces representing Laplace equations.-
    74. The hyperbolic case.-
    75. The parabolic case.-
    76. Surfaces representing differential equations of arbitrary order.-
    77. Varieties of arbitrary dimension representing Laplace equations.-
    78. Generalized developables.-
    79. Varieties of arbitrary order representing differential equations of arbitrary order.-
    80. The postulation of varieties by conditions on their r-osculating spaces.- Historical Notes and Bibliography.- Ten. Correspondences between Topological Varieties.-
    81. Products of topological varieties.-
    82. Correspondences and relations.-
    83. Inverse correspondences.-
    84. Homologous correspondences.-
    85. Topological invariants of correspondences between topological varieties.-
    86. Arithmetic and algebraic invariants.-
    87. Geometric invariants.-
    88. i-correspondences on topological varieties.-
    89. Semiregular correspondences and their products.-
    90. Characteristic integers of a semi-regular correspondence.-
    91. Involutory elementary s-correspondences.-
    92. Algebraic and skew-algebraic involutory transformations.-
    93. An extension of Zeuthen’s formula to the topological domain.-
    94. One-valued elementary correspondences.-
    95. Correspondences represented by differentiable varieties.- Historical Notes and Bibliography.- Author Index.- Analytic Index.