arXiv subjects
Publications and source records attributed to Ercüment Ortaçgil.
The below discussion is in three sections A, B, C, each section in two parts I, II, I representing the standpoint of bundles with connections and II representing the standpoint of prehomogeneous geometries (phg's). In A, our object of study is a fibered manifold, in B its k-jet bundle and in C a general nonlinear PDE.
We study the Hadwiger-Alesker finiteness theorem from the standpoint of Lie theory and announce a generalization.
We outline a simple proof of PC without surgeries using the homogeneous flow introduced in [O].
Motivated by the Hamilton's Ricci flow, we define the homogeneous flow of a parallelizable manifold and show the long time existence and uniqueness of its solutions on $[0,\infty).$ Using this flow, we outline a simple proof of the Poincare Conjecture.
This note is an extended version of my presentation at the "Focused Research Workshop on Exterior Di§erential Systems and Lie Theory" held at the Fields Institute in Toronto, December 9-13, 2013. Some ideas and constructions of this note crystallized during my communication with Anthony D. Blaom. I am deeply grateful to him and also to P.J. Olver for his constant help and encouragement.
We define and study the invariant linear and nonlinear horizontal double complexes of a local Lie group.
Historically tensor calculus emerged in an attempt to formalize Rie- mann's ideas. We show that tensor calculus can be based also on Lie's idea of a transformation group and this approach leads quite naturally to the concept of deformation of a transformation group and the Kodaira- Spencer map.
We outline a framework which generalizes Felix Klein's Erlanger Programm which he announced in 1872 after exchanging ideas with Sophus Lie.