This Letter introduces a novel method for investigating the hyper-line of conically intersecting geometries in chemical systems. It also reports an example of reaction path calculation restricted to this hyper-line. A rigorous set of methods, based on constrained molecular dynamics and their variational counterpart, is developed to characterize the connectivity and the topology of conical intersection (CI) seams on a more quantitative issue with respect to all the work done till now in literature. As test case we characterize the topology of the manifold of conically intersecting geometries in the ethylene molecule, by performing a molecular dynamics with the degeneracy constraint (E-2 = E-1). (C) 2004 Elsevier B.V. All rights reserved.