We analyze the stability of geodesic curves in geometry Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole, describing space time a charged hole low energy limit string theory. The analysis is performed by using both linear (Lyapunov) method, as well notion Jacobi stability, based on Kosambi–Cartan–Chern Brief reviews two methods are also presented. After obtaining equations spherical symme...

Berwald geometries are Finsler close to (pseudo)-Riemannian geometries. We establish a simple first order partial differential equation as necessary and sufficient condition, which given Lagrangian has satisfy be of type. Applied $(\alpha,\beta)$-Finsler spaces, respectively $(A,B)$-Finsler spacetimes, this reduces condition for the Levi-Civita covariant derivative defining $1$-form. illustrate...

The notion of general weighted Ricci curvatures appears naturally in many problems. N-Ricci curvature and the projective are just two special ones with totally different geometric meanings. In this paper, we study curvatures. We find that Randers metrics certain isotropic must have S-curvature. Then classify them via their navigation expressions. also equations characterize almost curvature.

There are three distinct questions associated with Simpson’s paradox. (i) Why or in what sense is Simpson’s paradox a paradox? (ii) What is the proper analysis of the paradox? (iii) How one should proceed when confronted with a typical case of the paradox?We propose a “formal” answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding...

The curves, of which the square of the distance between the two points equal to zero, are called minimal or isotropic curves [4]. In this work, first, necessary and sufficient conditions to be a Pseudo Helix, which is a special case of such curves, are presented. Thereafter, it is proven that an isotropic curve’s position vector and pseudo curvature satisfy a vector differential equation of fou...

The aim of this work is to show a Berwald type inequality for the extremal universal integrals based on (α ,m) concave function. Some examples are given to illustrate the validity of these inequalities.

A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach de Sitter space. The action for this theory is obtained by a higher-derivative modification of Einstein s theory. We expect that our model can easily be gen...

We show that a closed orientable Riemannian n-manifold, n ≥ 5, with positive isotropic curvature and free fundamental group is homeomorphic to the connected sum of copies of S × S.

A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach de Sitter space. The action for this theory is obtained by a higher derivative modification of Einstein's theory. We expect that our model can easily be gen...