Isotropic Geometry of Graph Surfaces Associated with Product Production Functions in Economics

A production function is a mathematical formalization in economics which denotes the relations between the output generated by a firm, an industry or an economy and the inputs that have been used in obtaining it. In this paper, we study the product production functions of 2 variables in terms of the geometry of their associated graph surfaces in the isotropic 3-space I-3. In particular, we derive several classification results for the graph surfaces of product production functions in I-3 with constant curvature

Singular Minimal TranslationSurfaces in Euclidean Spaces Endowed with Semi-symmetric Connections

In this paper, we study and classify singular minimal translation surfaces in a Euclidean space of dimension $3$ endowed with a certain semi-symmetric (non-)metric connection

Affine Translation Surfaces in the Isotropic 3-Space

In this paper, we describe (linear) Weingarten affine translation surfaces of first kind in the isotropic 3-space. In addition, we obtain such surfaces that satisfy certain equations in terms of the position vector and the Laplace operator

Affine Translation Surfaces in the Isotropic 3-Space

In this paper, we describe (linear) Weingarten affine translation surfaces of first kind in the isotropic 3-space. In addition, we obtain such surfaces that satisfy certain equations in terms of the position vector and the Laplace operator

A classication of homothetical hypersurfaces in Euclidean spaces via Allen determinants and its applications

The present authors, in [3], classied the composite functions of the form f = F (h1 (x1) × ... × hn (xn)) via the Allen determinants used to calculate the Allen's elasticity of substitution of production functions in microeconomics. In this paper, we adapt this classication to the homothetical hypersurfaces in the Euclidean spaces. An application for the homothetical hypersurfaces is also given. © Balkan Society of Geometers, Geometry Balkan Press 2015

Affine Factorable Surfaces in Isotropic Spaces

In this paper, we study the problem of finding affine factorable surfaces in a 3-dimensional isotropic space I-3 with prescribed Gaussian (K) or mean (H) curvatures. Because the absolute figure of I-3, by permutation of coordinates two different types of these surfaces appear. We firstly classify the affine factorable surfaces of type 1 with K;H constants. Afterwards, we provide the affine factorable surfaces of type 2 with K = const: or H = 0: Besides in some particular cases, the affine factorable surfaces of type 2 with H = const were obtained

Singular minimal translation graphs in euclidean spaces

In this paper, we consider the problem of finding the hypersurface Mn in the Euclidean (n + 1)-space Rn+1 that satisfies an equation of mean curvature type, called singular minimal hypersurface equation. Such an equation physically characterizes the surfaces in the upper halfspace R3+(u) with lowest gravity center, for a fixed unit vector u?R3 . We first state that a singular minimal cylinder Mn in Rn+1 is either a hyperplane or a ?-catenary cylinder. It is also shown that this result remains true when Mn is a translation hypersurface and u is a horizantal vector. As a further application, we prove that a singular minimal translation graph in R3 of the form z = f(x) + g(y + cx), c ? R ? {0}, with respect to a certain horizantal vector u is either a plane or a ?-catenary cylinder. © 2021 Korean Mathematical Society

Pythagorean Isoparametric Hypersurfaces in Riemannian and Lorentzian Space Forms

We introduce the notion of a Pythagorean hypersurface immersed into an n+1-dimensional pseudo-Riemannian space form of constant sectional curvature c∈−1,0,1. By using this definition, we prove in Riemannian setting that if an isoparametric hypersurface is Pythagorean, then it is totally umbilical with sectional curvature φ+c, where φ is the Golden Ratio. We also extend this result to Lorentzian ambient space, observing the existence of a non totally umbilical model

Classification of Factorable Surfaces in the Pseudo-Galilean Space

In this paper, we introduce the factorable surfaces in the pseudo-Galilean space G(3)(1) and completely classify such surfaces with null Gaussian and mean curvature. Also, in a special case, we investigate the factorable surfaces which fulfill the condition that the ratio of the Gaussian curvature and the mean curvature is constant in G(3)(1)

Translation Surfaces In Pseudo-Galilean Space With Prescribed Mean And Gaussıan Curvatures

We study the translation surfaces in the pseudo–Galilean space with the condition that one of generating curves is planar. We classify these surfaces whose mean and Gaussian curvatures are functions of one variabl