arXiv subjects

Carlos Alberto Marín Arango

Publications and source records attributed to Carlos Alberto Marín Arango.

4 recordsLinked to original sources

arXiv2026

Infinitesimmaly homogeneous manifolds with symplectic and almost contact structure groups

We study infinitesimally homogeneous affine manifolds with prescribed structure groups. First, for the real symplectic group $\operatorname{Sp}(2n,\mathbb R)$, we prove that the corresponding infinitesimally homogeneous structures are precisely flat torsion-free symplectic affine structures. Second, for $\operatorname{U}(n)\times\{1\}$, whose $G$-structures are equivalent to almost contact metric data, we classify the torsion-free characteristic tensors and obtain the general torsional case by invariant deformation. The admissible torsion and inner-torsion parameters are governed by a single algebraic relation, and the horizontal distribution is contact precisely when a certain combination of these parameters does not vanish. We also describe the compatible connections and relate the torsion-free branches to trans-Sasakian geometry.

math.DG↗

arXiv2019

Homogeneous surfaces admitting invariant connections

We compute all the simply connected homogeneous and infinitesimally homogeneous surfaces admitting one or more invariant affine connections. We find exactly six non equivalent simply connected homogeneous surfaces admitting more than one invariant connections and four classes of simply connected homogeneous surfaces admitting exactly one invariant connection.

math.DG↗

arXiv2016

Closed and asymptotic formulas for energy of some circulant graphs

We consider circulant graphs G(r,N) where the vertices are the integers modulo N and the neighbours of 0 are {-r,...,-1,1,...,r}. The energy of G(r,N) is a trigonometric sum of N*r terms. For low values of r we compute this sum explicitly. We also study the asymptotics of the energy of G(r,N) for big N. There is a known integral formula for the linear growth coefficient, we find a new expression of the form of a finite trigonometric sum with r terms. As an application we show that in the family G(r,N) for r less or equal than 4 there is a finite number of hyperenergetic graphs. On the other hand, for each r>4 there is at most a finite number of non-hyperenergetic graphs of the form G(r,N). Finally we show that the graph G(r,2r+1) minimizes the energy among all the regular graphs of degree 2r.

math.CO↗

arXiv2016

Infinitesimally homogeneous manifolds with prescribed structure groups

We explore the class of triples (M, nabla, P) where M is a manifold, nabla is an affine connection in M and P is a G-structure in M. Inside this class there are infinitesimally homogeneous manifolds, characterized by having G-constant curvature, torsion and inner torsion. For each matrix Lie group G subgroup of GL(Rn) there is a class of infinitesimally homogeneous manifolds with structure group G. In this paper we characterize the classes of infinitesimally homogeneous manifolds for some specific values of the structure group G including: identity group, finite groups, diagonal group, special linear group, orthogonal group and unitary group.

math.DG↗