Geometry, Volume 2, Issue 4

It is well known among geometry scholars that the golden triangle, an isosceles triangle with sides and base in golden ratio, maintains a significant relationship with regular polygons, notably the regular pentagon, pentagram, and decagon. Extensive...

In the present paper, we give a simple proof of the Chen–Ricci inequality for submanifolds in Riemannian and Lorentzian space forms, respectively. Moreover, we extend the Chen–Ricci inequality to submanifolds in Lorentzian manifolds with...

We prove that if we start with a non-continuous absolute plane, remove Side-Angle-Side as an axiom, and replace it with the three new axioms, Side-Angle-Angle, angle addition, and the existence of angle bisectors, then the result is also an absolute...

In recent years, two quite different tools have been employed to study global properties of arcs in the plane. The first is drapeability, which grew from ideas of J. R. Alexander in early 2000s defining an arc drapeable if it lies in the convex hull...

We study the existence of Killing vector fields for right-invariant metrics on low-dimensional Lie groups. Specifically, Lie groups of dimension two, three and four are considered. Before attempting to implement the differential conditions that compr...

There exists an extensive and fairly comprehensive discrete analytic function theory which is based on circle packing. This paper introduces a faithful discrete analogue of the classical Schwarzian derivative to this theory and develops its basic pro...