in this paper, we study a special class of generalized douglas-weyl metrics whose douglas curvature is constant along any finslerian geodesic. we prove that for every landsberg metric in this class of finsler metrics, ? = 0 if and only if h = 0. then we show that every finsler metric of non-zero isotropic flag curvature in this class of metrics is a riemannian if and only if ? = 0.

A transformation of an n-dimensional Riemannian manifold M , which transforms every geodesic circle of M into a geodesic circle, is called a concircular transformation. A concircular transformation is always a conformal transformation. Here geodesic circle means a curve in M whose first curvature is constant and second curvature is identically zero. Thus, the geometry of concircular transformat...

Abstract For a smooth strongly convex Minkowski norm $F:\mathbb {R}^n \to \mathbb {R}_{\geq 0}$ , we study isometries of the Hessian metric corresponding to function $E=\tfrac 12F^2$ . Under additional assumption that F is invariant with respect standard action $SO(k)\times SO(n-k)$ prove conjecture Laugwitz stated in 1965. Furthermore, describe all between such metrics, and Landsberg Unicorn C...

we prove that every r-quadratic metric of scalar flag curvature with a dimension greater than twois of constant flag curvature. then we show that generalized douglas-weyl metrics contain r-quadraticmetrics as a special case, but the class of r-quadratic metric is not closed under projective transformations

The circadian clock is an important determinant of fitness that entrained by local conditions. Aside from abiotic factors, individual pathogenic soil bacteria affect function in plant hosts. Yet, nature, plants interact with diverse microbial communities, and the effect complex communities on remains unclear. In Arabidopsis thaliana its wild relative, Boechera stricta, we used rhizosphere inocu...

This work is a generalization of the López-Ruiz, Mancini and Calbet (LMC); and Shiner, 1 Davison and Landsberg (SDL) complexity measures, considering that the state of a system or process 2 is represented by a dynamical variable during a certain time interval. As the two complexity 3 measures are based on the calculation of informational entropy, an equivalent information source 4 is defined an...

A two-parameter family of statistical measures of complexity are introduced based on the Tsallis-type nonadditive entropies. This provides a unified framework for the study of the recently proposed various measures of complexity as well as for the discussion of a whole new class of measures. As a special case, a generalization of the measure proposed by Landsberg and his co-workers based on the...