3 papers
math.DG2022
On Hadwiger-Alesker finiteness theorem
Ercüment Ortaçgil
We study the Hadwiger-Alesker finiteness theorem from the standpoint of Lie theory and announce a generalization.
math.DG2014
The homogeneous flow of a parallelizable manifold
Ercüment Ortaçgil
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).…
math.DG2010
Riemannian geometry as a curved pre-homogeneous geometry
Ercument Ortacgil
We define a Riemannian structure as a pre-homogeneous geometric structure with curvature R. We show that R=0 if and only if the underlying metric has constant curvature. We define…