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.
Highlights
Modern differential geometry plays an important role to explain the dynamics of Lagrangians
If Q is an m-dimensional configuration manifold and L : TQ R is a regular Lagrangian function, it is well-known that there is a unique vector field X on TQ such that dynamics equation is given by iX L = dEL
Modern differential geometry provides a good framework in which develop the dynamics of Hamiltonians
Summary
Modern differential geometry plays an important role to explain the dynamics of Lagrangians. If Q is an m-dimensional configuration manifold and L : TQ R is a regular Lagrangian function, it is well-known that there is a unique vector field X on TQ such that dynamics equation is given by iX L = dEL (1). There are many studies about Lagrangian and Hamiltonian dynamics, mechanics, formalisms, systems and equations [1,2,3,4,5] and there in. By a Walker n-manifold, we mean a semi-Riemannian manifold which admits a field of parallel null r-planes, with r. 2m) admitting a field of null planes of maximum dimensionality(r = m). We present complex (paracomplex) analogues of Lagrangian and Hamiltonian mechanical systems on 4-Walker manifold. TEKKOYUN tions on M4, the set of vector fields on M4 and the set of 1-forms on M4, respectively
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