TITLE:
A Survey on Geometric Dynamics of 4-Walker Manifold
AUTHORS:
Mehmet Tekkoyun
KEYWORDS:
Walker Manifolds, Lagrangian and Hamiltonian Mechanics
JOURNAL NAME:
Journal of Modern Physics,
Vol.2 No.11,
November
23,
2011
ABSTRACT: A Walker n-manifold is a semi-Riemannian n-manifold, which admits a field of parallel null r-planes, with r ≤ 2/n . It is well-known that semi-Riemannian geometry has an important tool to describe spacetime events. Therefore, solutions of some structures about 4-Walker manifold can be used to explain spacetime singularities. Then, here we present complex and paracomplex analogues of Lagrangian and Hamiltonian mechanical systems on 4-Walker manifold. Finally, the geometrical-physical results related to complex (paracomplex) mechanical systems are also discussed.