## On certain properties of the metrical and generalized metrical groups in linear spaces of n dimensions |

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### Contents

ection Chapter 1 Page 1 Introduction | 1 |

Extension of Eulers formulae | 2 |

Certain properties of Eulers transformation | 4 |

14 other sections not shown

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absolutely invariant absolutely orthogonal set aeolotropic spaces ametric manifolds angle of rotation angles 12 arbitrary functions Cayley coefficients cofactor College of Washington Columbia University condition of orthogonality conjugate const coordinates cos(n cos/»_2 dxi defined Differential Geometry differential invariants direction cosines dxdx dydy element of length equal to zero equation 57 Fn-i fundamental metrical form gonal group of rotations hence hyperplane idXi idxt independent parameters invariant planes Kasner Kowalewski linear threads Mathematical matrix metrical group Monge's equation null curves null geometry null lines null subflats obtain the following order determinants ordinary orthogonal group ortho orthogonal straight lines perpendicular point in Fn properties prove the theorem rank reciprocal determinant remain invariant rotation in Fn set of equations set of planes simple rotations simply orthogonal set Sl S2 S8 subgroup Substituting successive rotations trans vanish