On Certain Properties of the Metrical and Generalized Metrical Groups in Linear Spaces of N Dimensions |
Other editions - View all
Common terms and phrases
1+mn a₁ a¹¹ absolutely invariant absolutely orthogonal set Ak+2 ametric manifolds angle of rotation angles 12 arbitrary functions B₁ C₁ C₂ Cg S5 C6 Cg S6 coefficients cofactor College of Washington Columbia University condition of orthogonality conjugate const coördinates cos 3 n cosio defined Differential Geometry differential invariants direction cosines DOCTOR OF PHILOSOPHY dxdx dydy element of length equal to zero equation 57 f₂ flat fundamental metrical form gonal group of rotations hence independent parameters invariant planes Kasner Kowalewski m₁ matrix metrical group Monge's equation null curves null geometry null lines null plane null subflats ordinary orthogonal group orthogonal straight lines P² Q² Pir Pir rotation in Fn S₁ set of equations set of planes simple rotations simply orthogonal set sin 1 n Substituting transformations x₁ x₂ Y₁ Y₂