Mihail Cocos

collaborators

3 papers

math.DG2025

Proof of Chern conjecture for flat affine manifolds

Mihail Cocos

We prove Chern conjecture, which states that the Euler characteristic vanishes for closed flat affine manifolds. Our key innovation is a deformation argument for the Euler form.

math.DG2025

Affine-Orthogonal Manifolds and Deformation to Levi-Civita Connections

Mihail Cocos

We study a class of affine manifolds equipped with a flat affine connection $\nabla$ and a global Riemannian metric $g$ that is diagonal in local affine coordinates. These structur…

math.DG2025

A Riemannian Characterization of Compact Affine Manifolds with Parallel Volume

Mihail Cocos

We establish that any affine manifold $(M, \nabla)$ endowed with a parallel volume form $I ¨ ,$ admits, in any conformal class of Riemannian metrics, a representative $H$ for which $\…