9 papers
Affine-Orthogonal Manifolds and Deformation to Levi-Civita Connections
Mihail Cocos
We study a class of affine manifolds equipped with a flat affine connection and a global Riemannian metric that is diagonal in local affine coordinates. These structur…
A Riemannian Characterization of Compact Affine Manifolds with Parallel Volume
Mihail Cocos
We establish that any affine manifold endowed with a parallel volume form admits, in any conformal class of Riemannian metrics, a representative for which $\n…
Skewable matrices over applied to locally metric connections
Mihail Cocos, Kent Kidman
A necessary condition for a connection in a vector bundle to be locally metric is for its curvature matrix, which consists of forms, to be skew symmetric with respect to some l…
A note on locally metric connections
Mihail Cocos
In this paper we give necessary and sufficient conditions for a connection in a plane bundle above a surface to be locally metric. These conditions are easy to be verified in any l…
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.
Zero sets and factorization of polynomials of two variables
Micki Balaich, Mihail Cocos
The relationship between a polynomial's zeros and factors is well known. If a is a zero of f(x) then (x-a) is a factor of f(x). In this paper, we generalize this idea to polynomial…
Musical Modes, Their Associated Chords and Their Musicality
Mihail Cocos, Kent Kidman
In this paper we present a mathematical way of defining musical modes and we define the musicality of a mode as a product of three different factors. We conclude by classifying the…
Music By Numbers
Mihail Cocos, Shawn Fowers
In this paper we present a mathematical way of defining musical modes, we derive a formula for the total number of modes and define the musicality of a mode as the total number of…
On the topology of compact affine manifolds
Mihail Cocos
Geodesically complete affine manifolds are quotients of the Euclidean space through a properly discontinuous action of a subgroup of affine Euclidean transformations. An equivalent…