...ov Hydrodynamic Covariant Symp- lectic Structure from Bilinear Hamiltonian Functions. . . . . . . . . . . . . . . . . . . . 92 D. Rabounski, L. Boriss... ...nal feld are the proper radius and the curvature radius, both of which are functions of r. The variable r is actually a Euclidean parameter which is m... ...r)dr 2 −C(r) dθ 2 +sin 2 θdϕ 2 , (2a) A,B,C>0, whereA,B,C are analytic functions. I emphatically remark that the geometric relations between the c... ...+dz 2 − −H |x−x 0 |dx+|y−y 0 |dy+|z−z 0 |dz 2 , (5) whereF,G,H>0 are functions of D= q |x−x 0 | 2 +|y−y 0 | 2 +|z−z 0 | 2 =|r−r 0 |, andP 0 (x 0... ... = =A(D)dt 2 −B(D)dr 2 −C(D) dθ 2 +sin 2 θdϕ 2 , (6) where A,B,C>0 are functions of D=|r−r 0 |. Equation (6) is just equation (2a), but equation (... ...he reason that we will consider situations derived from different factors, generating gravita- tional wave felds, not only the space deformation. The ... ...th the ground ( most stable ) state of the Hydrogen atom [3]. The spectrum generating group of the Hydrogen atom is well known to be the conformal gro... ...iant canonical symplectic structure. The variation (67) may be seen as the generating functionG of canonical transformations where the generators ofq−...