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

We consider spacetime to be a connected real 4-manifold equipped with a Lorentzian metric and an affine connection. The 10 independent components of the (symmetric) metric tensor and the 64 connection coefficients are the unknowns of our theory. We introduce an action which is quadratic in curvature and study the resulting system of Euler–Lagrange equations. In the first part of the paper we lo...

We investigate the cosmological aspects of most general parity preserving Metric-Affine Gravity theory quadratic in torsion and non-metricity presence a hyperfluid. The equations motion are obtained by varying action with respect to metric independent affine connection. Subsequently, considering Friedmann-Lema\^itre-Robertson-Walker background, we derive form modified Friedmann for full theory....

In the general framework of Metric-Affine theories gravity, where metric and connection are independent variables, we consider actions quadratic in Ricci scalar curvature Holst invariant (the contraction Riemann with Levi-Civita antisymmetric tensor) coupled non-minimally to a field. We study profile equivalent effective theory, featuring an extra dynamical pseudoscalar degree freedom, show tha...

in this paper, we prove the generalized hyers-ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-archimedean $mathcal{l}$-fuzzy normed spaces.

In this work we study the stability of four vector irreducible pieces torsion and nonmetricity tensors in general quadratic metric-affine Lagrangian 4 dimensions. The goal will be to elucidate under which conditions spin-1 modes associated such vectors can propagate a safe way, together with graviton. This highly constrains theory reducing parameter space curvature part from 16 5 parameters. We...

1. Teichm uller space and the Teichm uller metric d(X; Y) = inf(1=2) log K(), where : X ! Y ranges over all quasiconformal mappings in the appropriate isotopy class. 2. Teichm uller's theorem: If X is compact, or more generally if X is obtained from a compact Riemann surface by removing a nite number of points, then there is an essentially map f minimizing the innmum above. (This map is unique ...

This paper studies the smoothness and curvature of a marginal function for a trust-region problem. In this problem, a quadratic function is minimized over an ellipsoid. The marginal function considered is obtained by perturbing the trust radius, i.e., by changing the size of the ellipsoidal constraint. The values of the marginal function and of its rst and second derivatives are explicitly calc...