A Survey on Geometric Dynamics of 4-Walker Manifold

Mehmet Tekkoyun

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DOI: 10.4236/jmp.2011.211163                

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.

Keywords

Walker Manifolds, Lagrangian and Hamiltonian Mechanics

Conflicts of Interest

The authors declare no conflicts of interest.

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