Killing-Yano symmetry for a class of spacetimes admitting parallel null 1-planes

A possible generalization of plane fronted waves with parallel rays (gpp-wave) fall into a more general class of metrics admitting parallel null 1-planes. For gpp-wave metric, the zero-curvature condition is given, the Killing-Yano tensors of order two and three are found and the corresponding Killing tensors are constructed. Henceforth, the compatibility between geometric duality and non-generic symmetries is presented.Comment: 11 pages, LaTeX, to be published in Il Nuovo Cimento

Dual Metrics and Non-Generic Supersymmetries for a Class of Siklos Spacetimes

The presence of Killing-Yano tensors implies the existence of non-generic supercharges in spinning point particle theories on curved backgrounds. Dual metrics are defined through their associated non-degenerate Killing tensors of valence two. Siklos spacetimes, which are the only non-trivial Einstein spaces conformal to non-flat pp-waves are investigated in regards to the existence of their corresponding Killing and Killing-Yano tensors. It is found that under some restrictions, pp-wave metrics and Siklos spacetimes admit dual metrics and non-generic supercharges. Possible significance of those dual spacetimes are discussed.Comment: LaTeX, 8 page

Fractional Analogous Models in Mechanics and Gravity Theories

We briefly review our recent results on the geometry of nonholonomic manifolds and Lagrange--Finsler spaces and fractional calculus with Caputo derivatives. Such constructions are used for elaborating analogous models of fractional gravity and fractional Lagrange mechanics.Comment: latex2e, 11pt, 11 pages with table of content; it is summary of the results presented in our talk at the 3d Conference on "Nonlinear Science and Complexity", 28--31 July, 2010, \c{C}hankaya University, Ankara, Turke

Metafluid dynamics and Hamilton-Jacobi formalism

Metafluid dynamics was investigated within Hamilton-Jacobi formalism and the existence of the hidden gauge symmetry was analyzed. The obtained results are in agreement with those of Faddeev-Jackiw approach.Comment: 7 page

Cosmological perturbations in FRW model with scalar field within Hamilton-Jacobi formalism and symplectic projector method

The Hamilton-Jacobi analysis is applied to the dynamics of the scalar fluctuations about the Friedmann-Robertson-Walker (FRW). The gauge conditions are found from the consistency conditions. The physical degrees of freedom of the model are obtain by symplectic projector method. The role of the linearly dependent Hamiltonians and the gauge variables in Hamilton-Jacobi formalism is discussed.Comment: 11 page

Fractional Exact Solutions and Solitons in Gravity

We survay our recent results on fractional gravity theory. It is also provided the Main Theorem on encoding of geometric data (metrics and connections in gravity and geometric mechanics) into solitonic hierarchies. Our approach is based on Caputo fractional derivative and nonlinear connection formalism.Comment: latex2e, 11pt, 10 pages with table of content; a summary of our talk at Conference "New Trends in Nanotechnology and Nonlinear Dynamical Systems", 25--27 July, 2010, \c{C}ankaya University, Ankara, Turke