arXiv subjects

M. Castrillón López

Publications and source records attributed to M. Castrillón López.

3 recordsLinked to original sources

arXiv2021

Rigid Body with Rotors and Reduction by Stages

Rigid body with rotors is a widespread mechanical system modeled after the direct product $SO(3)\times S^1\times S^1\times S^1$, which under mild assumptions is the symmetry group of the system. In this paper, the authors present and compare different Lagrangian reduction procedures: Euler-Poincaré reduction by the whole group and reduction by stages in different orders or using different connections. The exposition keeps track of the equivalence of equations as well as corresponding conservation laws.

math-ph↗

arXiv2013

Homogeneous structures of linear type on $ε$-Kähler and $ε$-quaternion Kähler manifolds

We analyze degenerate homogeneous structures of linear type in the pseudo-Kähler and para-Kähler cases. The local form and the holonomy of pseudo-Kähler or para-Kähler manifolds admitting such structure are obtained. In addition the associated homogeneous models are studied exhibiting their relation with the incompleteness of the metric. The same questions are tackled in the pseudo-quaternion Kähler and para-quaternion Kähler cases. These results complete the study of homogeneous structures of linear type in pseudo-Kähler, para-Kähler, pseudo-quaternion Kähler and para-quaternion Kähler cases.

math.DG↗

arXiv2012

Strongly degenerate homogeneous pseudo-Kähler structures of linear type and complex plane waves

We study the class $\mathcal{K}_{2}+\mathcal{K}_{4}$ of homogeneous pseudo-Kähler structures in the strongly degenerate case. The local form and the holonomy of a pseudo-Kähler manifold admitting such a structure is obtained, leading to a possible complex generalization of homogeneous plane waves. The same question is tackled in the case of pseudo-hyper-Kähler and pseudo-quaternion Kähler manifolds.

math.DG↗