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Transformation of coordinates |
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1 | (2) |
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Coefficients of connection |
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3 | (2) |
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Covariant differentiation with respect to the L's |
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5 | (2) |
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Generalized identities of Ricci |
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7 | (1) |
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Other fundamental tensors |
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8 | (3) |
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Covariant differentiation with respect to the I's |
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11 | (1) |
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12 | (2) |
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A theorem on partial differential equations |
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14 | (4) |
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Fields of parallel contra variant vectors |
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18 | (4) |
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Parallel displacement of a contravariant vector around an infinitesimal circuit |
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22 | (5) |
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Pseudo-orthogonal contravariant and covariant vectors. Parallelism of covariant vectors |
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27 | (2) |
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Changes of connection which preserve parallelism |
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29 | (6) |
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Tensors independent of the choice of ψ |
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35 | (1) |
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Semi-symmetric connections |
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36 | (2) |
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Transversals of parallelism of a given vector-field and associate vector-fields |
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38 | (5) |
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43 | (1) |
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Determination of a tensor by an ennuple of vectors and invariants |
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44 | (3) |
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The invariants γ νμσ of an ennuple |
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47 | (3) |
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Geometric properties expressed in terms of the invariants νμσ |
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50 | (3) |
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53 | (2) |
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The curvature tensor and other fundamental tensors |
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55 | (1) |
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56 | (2) |
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58 | (4) |
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62 | (2) |
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Extension of the theorem of Fermi to symmetric connections |
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64 | (4) |
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68 | (4) |
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72 | (2) |
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The equivalence of symmetric connections |
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74 | (4) |
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Riemannian spaces. Flat spaces |
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78 | (3) |
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Symmetric connections of Weyl |
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81 | (2) |
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Homogeneous first integrals of the equations of the paths |
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83 | (4) |
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Projective Geometry of Paths |
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Projective change of affine connection. The Weyl tensor |
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87 | (4) |
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Affine normal coordinates under a projective change of connection |
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91 | (3) |
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94 | (4) |
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Coefficients of a projective connection |
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98 | (2) |
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The equivalence of projective connections |
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100 | (4) |
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104 | (2) |
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Projective parameters of a path |
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106 | (1) |
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Coefficients of a projective connection as tensors |
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107 | (3) |
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110 | (1) |
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Projective normal coordinates |
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111 | (5) |
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Significance of a projective change of affine connection |
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116 | (1) |
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Homogeneous first integrals under a projective change |
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117 | (2) |
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Spaces for which the equations of the paths admit n(n+1)/2 independent homogeneous linear first integrals |
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119 | (3) |
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Transformations of the equations of the paths |
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122 | (2) |
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Collineations in an affinely connected space |
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124 | (5) |
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Conditions for the existence of infinitesimal collineations |
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129 | (4) |
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Continuous groups of collineations |
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133 | (1) |
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Collineations in a Riemannian space |
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134 | (3) |
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The Geometry of Sub-Spaces |
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Covariant pseudonormal to a hypersurface. The vector-field να |
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137 | (4) |
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Transversals of a hypersurface which are paths of the enveloping space |
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141 | (2) |
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Tensors in a hypersurface derived from tensors in the enveloping space |
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143 | (5) |
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Symmetric connection induced in a hypersurface |
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148 | (2) |
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Fundamental derived tensors in a hypersurface |
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150 | (2) |
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The generalized equations of Gauss and Codazzi |
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152 | (2) |
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Contravariant pseudonormal |
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154 | (4) |
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Fundamental equations when the determinant ω is not zero |
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158 | (2) |
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Parallelism and associate directions in a hypersurface |
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160 | (2) |
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Curvature of a curve in a hypersurface |
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162 | (1) |
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Asymptotic lines, conjugate directions and lines of curvature of a hypersurface |
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163 | (3) |
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Projectively flat spaces for which Bij is symmetric |
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166 | (4) |
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Covariant pseudonormals to a sub-space |
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170 | (1) |
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Derived tensors in a sub-space. Induced affine connection |
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171 | (1) |
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Fundamental derived tensors in a sub-space |
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172 | (3) |
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Generalized equations of Gauss and Codazzi |
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175 | (2) |
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Parallelism in a sub-space. Curvature of a curve in a sub-space |
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177 | (1) |
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Projective change of induced connection |
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178 | (3) |
| Bibliography |
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181 | |
Other versions by this Author
