Related papers: A geometric identity for Pappus' Theorem

Group lattices (Cayley digraphs) of a discrete group are in natural correspondence with differential calculi on the group. On such a differential calculus geometric structures can be introduced following general recipes of noncommutative…

This work presents for the first time a solution to the 1821 unsolved Sawa Masayoshi's problem, giving an explicit and algebraically exact solution for the symmetric case (particular case b = c, i.e., ABC \equiv right-angled isosceles…

We prove that the Riemannian geometry of almost K\"ahler manifolds can be expressed in terms of the Poisson algebra of smooth functions on the manifold. Subsequently, K\"ahler-Poisson algebras are introduced, and it is shown that a…

Recently, it has been shown that Absolute Parallelism (AP) geometry admits paths that are naturally quantized. These paths have been used to describe the motion of spinning particles in a background gravitational field. In case of a weak…

Based on the Carath\'eodory -Pesin structure theory[11], we introduce three notions of topological pressure of a proper map and provide some properties of these notions. For the proper map of a locally compact separable metric space, we…

This essay, an excerpt of the author's Ph.D. in Philosophy of mathematics (2012) thought of as being a companion to recent discoveries of new explicit Cartan geometry curvatures, analyzes how Gauss, after having devised the isometrically…

We consider polynomial maps, which we call degree $d$-linear maps, that satisfy the Jacobian condition. We prove that certain infinite families of elements, which appear in the coefficients of the formal inverse of such maps, are in the…

The category of generalized Lie algebroids is presented. We obtain an exterior differential calculus for generalized Lie algebroids. In particular, we obtain similar results with the classical and modern results for Lie algebroids. So, a…

Einstein used 4-dimensional space time geometry to explain gravity. However, in 1962, Baierlein, Sharp and Wheeler proposed a Jacobi type timeless Lagrangian based on the 3-dimensional geometry of space to reproduce the same physics. In…

We give a uniform proof of a significant part of the Cachazo-Douglas-Seiberg-Witten conjecture by using topology and geometry of infinite Grassmannians.

The paper contains an exposition of part of topology using partitions of unity. The main idea is to create variants of the Tietze Extension Theorem and use them to derive classical theorems. This idea leads to a new result generalizing…

We give a simplified derivation of the expression of instanton numbers and of mirror map in terms of Frobenius map on p-adic cohomology and use this expression to prove integrality theorems. Modifying this proof we verify that the…

A variational principle was recently suggested by Goenner, where an independent metric generates the spacetime connection. It is pointed out here that the resulting theory is equivalent to the usual Palatini theory. However, a bimetric…

Covariant or invariant functions under a compact linear group can be expressed in terms of functions defined in the orbit space of the group. The semialgebraic relations defining the orbit spaces of all finite coregular real linear groups…

The dynamics of $N\geq 3$ interacting particles is investigated in the non-relativistic context of the Barbour-Bertotti theories. The reduction process on this constrained system yields a Lagrangian in the form of a Riemannian line element.…

We introduce geometric structures on the space of stability conditions of a three-dimensional Calabi-Yau category which encode the Donaldson-Thomas invariants of the category. We explain in detail a close analogy between these structures,…

For differential operators of Calabi-Yau type, Candelas, de la Ossa and van Straten conjecture the appearance of $p$-adic zeta values in the matrix entries of their $p$-adic Frobenius structure expressed in the standard basis of solutions…

These notes provide an account on four lectures given by Adrian Ioana at the Institut Henri Poincare in May 2011, regarding a number of "uniqueness of Cartan" type results obtained in a recent series of papers by Chifan-Peterson and…

We propose a formulation of gravity theory in the form of a field theory in a flat space-time with a number of dimensions greater than four. Configurations of the field under consideration describe the splitting of this space-time into a…

Roundness of metric spaces was introduced by Per Enflo as a tool to study uniform structures of linear topological spaces. The present paper investigates geometric and topological properties detected by the roundness of general metric…