The study of weakly symmetric and weakly projective symmetric manifold were initiated by Tamassy and Binh in 1989. Later on several authors studied weakly symmetric Riemannian manifold and analogous structures, viz. Weakly Ricci symmetric, weakly projective symmetric and weakly conformally symmetric Riemannian manifolds. At first we cited examples of weakly symmetric Riemannian manifolds. Next ...

We study the effect of infinitesimal onsite disorder on d-dimensional all bands flat lattices. The lattices are generated from diagonal Hamiltonians by a sequence (d + 1) local unitary transformations parametrized angles ${\theta}_i$. Without loss generality, we consider case two separated finite gap $\Delta$. perturbed states originating described an effective tight binding network with on- an...

We show that each R-module is n-flat (resp., weakly n-flat) if and only if R is an (n,n− 1)-ring (resp., a weakly (n,n− 1)-ring). We also give a new characterization of n-von Neumann regular rings and a characterization of weak n-von Neumann regular rings for (CH)-rings and for local rings. Finally, we show that in a class of principal rings and a class of local Gaussian rings, a weak n-von Neu...

It is given a complete study of locally conformally flat metrics satisfying some weakly-Einstein conditions. shown that they are either product Mn(c)×Mn(−c) or warped R×fRn−1 for specific warping function. Moreover, conditions on fixed points the RG2 flow pointed out.

The main goal of this paper is to reveal the geometric meaning of the maximal number of exceptional values of Gauss maps for several classes of immersed surfaces in space forms, for example, complete minimal surfaces in the Euclidean three-space, weakly complete improper affine spheres in the affine three-space and weakly complete flat surfaces in the hyperbolic three-space. For this purpose, w...