From [4] we continue the algebraic investigation of generalized and equiaffine curvature tensors in a given pseudo-Euclidean vector space and study different orthogonal, irreducible decompositions in analogy to the known decomposition of algebraic curvature tensors. We apply the decomposition results to characterize geometric properties of Codazzi structures and relative hypersurfaces; particul...

In this paper we study spherically symmetric metrics on a space in $\mathbb{R}^n$ with scalar and constant flag curvature also obtain families of type metrics. Many explicit examples are provided for Douglas curvature. Furthermore, new projectively flat Finsler given. We provide family which not type.

Abstract This paper is devoted to the study of asymptotics Monge–Ampère volumes direct images associated with high tensor powers an ample line bundle. We leading term this and provide a classification bundles saturating topological bound Demailly. In special case symmetric vector bundles, provides characterization those admitting projectively flat Hermitian structures.

An integral domain $D$ is called a emph{locally GCD domain} if $D_{M}$ is aGCD domain for every maximal ideal $M$ of $D$. We study somering-theoretic properties of locally GCD domains. E.g., we show that $%D$ is a locally GCD domain if and only if $aDcap bD$ is locally principalfor all $0neq a,bin D$, and flat overrings of a locally GCD domain arelocally GCD. We also show that the t-class group...

It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth, fiberwise-polynomial functions on the cotangent bundle a one-parameter family of graded star products. For a particular value of the parameter (corresponding to half-densities) the star product is symmetric, and specializes in the projectively flat case to the one constructed previ...

We will show that a statistical manifold $$(M, g, \nabla )$$ has constant curvature if and only it is projectively flat conjugate symmetric manifold, is, the affine connection $$\nabla $$ curvatures satisfies $$R=R^*$$ , where $$R^*$$ of dual ^*$$ . Moreover, we properly convex structures on compact induces $$-1$$ vice versa.

It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth functions on the cotangent bundle, fiberwise-polynomial of bounded degree, a one-parameter family of graded star products. For a particular value of the parameter (corresponding to half-densities) the star product is symmetric, and specializes in the projectively flat case to the on...