On Finslerian Hypersurfaces Given by β-Changes

V-REPRESENTATION FOR NORMALITY EQUATIONS in geometry of generalized Legendre transformation

Abstract. Normality equations describe Newtonian dynamical systems admitting normal shift of hypersurfaces. These equations were first derived in Euclidean geometry. Then very soon they were rederived in Riemannian and in Finslerian geometry. Recently I have found that normality equations can be derived in geometry given by classical and/or generalized Legendre transformation. However, in this ...

0 Ju n 20 14 Isometries , submetries and distance coordinates on Finsler manifolds

This paper considers fundamental issues related to Finslerian isometries, submetries, distance and geodesics. It is shown that at each point of a Finsler manifold there is a distance coordinate system. Using distance coordinates, a simple proof is given for the Finslerian version of the Myers–Steenrod theorem and for the differentiability of Finslerian submetries. AMS Subject Class. (2010): 53B40

Relativity Principles in 1+1 Dimensions and Differential Aging Reversal

We study the behavior of clocks in 1+1 spacetime assuming the relativity principle, the principle of constancy of the speed of light and the clock hypothesis. These requirements are satisfied by a class of Finslerian theories parametrized by a real coefficient β, special relativity being recovered for β = 0. The effect of differential aging is studied for the different values of β. Below the cr...

First stability eigenvalue characterization of Clifford hypersurfaces

ABSTRACT : The stability operator of a compact oriented minimal hypersurface Mn−1 ⊂ S is given by J = −∆ − ‖A‖ − (n − 1), where ‖A‖ is the norm of the second fundamental form. Let λ1 be the first eigenvalue of J and define β = −λ1 − 2(n − 1). In [S] Simons proved that β ≥ 0 for any non-equatorial minimal hypersurface M ⊂ S. In this paper we will show that β = 0 only for Clifford hypersurfaces. ...

Shen's Processes on Finslerian Connections