8 citations · 17 across the 8 of their papers we have counts for
9 papers
On projective symmetries on Finsler Spaces
Behnaz Lajmiri, Behroz Bidabad, Mehdi Rafie-Rad +1
There are two definitions of Einstein-Finsler spaces introduced by Akbar-Zadeh, which we will show is equal along the integral curves of -invariant projective vector fields. The…
Geometry of submanifolds of all classes of third-order ODEs as a Riemannian manifold
Z. Bakhshandeh-Chamazkoti, A. Behzadi, R. Bakhshandeh-Chamazkoti +1
In this paper, we prove that any surface corresponding to linear second-order ODEs as a submanifold is minimal in all classes of third-order ODEs as a Riemanni…
On the C-projective vector fields on Randers spaces
Azadeh Shirafkan, Mehdi Rafie-Rad
A characterization of the C-projective vector fields on a Randers spaces is presented in terms of a recently introduced non-Riemannian quantity defined by Z. Shen and denoted by ${…
Matsumoto metrics of constant flag curvature are trivial
M. Rafie-Rad, B. Rezaei
The local structure of Finsler metrics of constant flag curvature have been historically mysterious. It is proved that every Matsumoto metric of constant flag curvature on a manifo…
On the projective algebra of Einstein Matsumoto metrics
M. Rafie-Rad
The projective algebra p(M;F) (i.e the collection of all projective vector fields)of a Finsler space (M;F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket…
On the Projective Algebra of Randers Metrics of Constant Flag Curvature
Mehdi Rafie-Rad, Bahman Rezaei
The collection of all projective vector fields on a Finsler space is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra…
Time-Optimal solutions of Parallel Navigation and Finsler geodesics
M. Rafie-Rad
A geometric approach to kinematics in control theory is illustrated. A non-linear control system is derived for the problem and the Pontryagin maximum principle is used to find the…
On k-nullity foliations in Finsler geometry and completeness
B. Bidabad, M. Rafie-Rad
Here, a Finsler manifold (M, F) is considered with corresponding curvature tensor, regarded as 2-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent s…
Brachistochrone Pursuit - Evasion Games and Riemann-Finsler Geometry
Mehdi Rafie-Rad
A geometric approach to differential game theory is illustrated. The parallel pursuit is considered as a two-player zero-sum differential game. The optimal strategies of each playe…