Person: Pozo Coronado, Luis Miguel
Universidad Complutense de Madrid
Faculty / Institute
Geometría y Topología
Now showing 1 - 10 of 14
- PublicationCohomology of Horizontal Forms(Birkhäuser, 2012) Muñoz Masqué, Jaime; Pozo Coronado, Luis MiguelThe complex of s-horizontal forms of a smooth foliation F on a manifold M is proved to be exact for every s = 1, . . . , n = codim F, and the cohomology groups of the complex of its global sections, are introduced. They are then compared with other cohomology groups associated to a foliation, previously introduced. An explicit formula for an s-horizontal primitive of an s-horizontal closed form, is given. The problem of representing a de Rham cohomology class by means of a horizontal closed form is analysed. Applications of these cohomology groups are included and several specific examples of explicit computation of such groups-even for non-commutative structure groups-are also presented.
- PublicationHamilton equations for elasticae in the Euclidean 3-space.(Elsevier, 2000) Pozo Coronado, Luis MiguelThe variational problem on spatial curves defined by the integral of the squared curvature, whose solutions are the elasticae or nonlinear splines, is analyzed from the Hamiltonian point of view, using a procedure developed by Munoz Masqueand Pozo Coronado [J. Munoz Masque, LM. Pozo Coronado, J. Phys. A 31 (1998) 6225-6242]. The symmetry of the problem under rigid motions is then used to reduce the Euler-Lagrange equations to a first-order dynamical system.
- PublicationThe prescribed curvature problem in dimension four.(Elsevier, 2009) Muñoz Masqué, Jaime; Pozo Coronado, Luis Miguel; Sánchez Rodríguez, I.Necessary and sufficient conditions for a g-valued differential 2-form on a 4-dimensional manifold to be, locally, a curvature; form, are given. The dimension four is exceptional for the problem of prescribed curvature as, in this dimension, Bianchi's identities can be eliminated for a large class of Lie algebras, including semisimple algebras. Hence, the curvature forms are characterized as the solutions to a second-order partial differential system, which is proved to be formally integrable.
- PublicationElementos de Matemáticas y aplicaciones(No publicado, 2013) Castrillón López, Marco; Díaz-Cano Ocaña, Antonio; Etayo Gordejuela, J. Javier; Folgueira, Marta; Infante del Río, Juan Antonio; Pozo Coronado, Luis Miguel; Rey Cabezas, José MaríaMaterial elaborado por profesores de la UCM para la asignatura de este nombre del grado en Ingeniería Matemáticas, el grado en Matemáticas y el grado en Matemáticas y Estadística. Contenidos: - Números enteros. Dígitos de control y criptografía. - Grupos de simetrías. Mosaicos. - Trigonometría plana y esférica. Aplicaciones (Navegación, Astronomía de posición, GPS). - Dinámica discreta. Aplicaciones (Finanzas, introducción al caos). - Teoría de grafos. Algoritmo de ordenación de Google.
- PublicationGlobal characterization of variational first-order quasi-linear equations.(Elsevier, 2005) Muñoz Masqué, Jaime; Pozo Coronado, Luis MiguelThe global inverse problem of the calculus of variations for the particular case of first-order quasi-linear PDEs is solved. Some examples in the field theory are discussed.
- PublicationParameter invariance in field theory and the Hamiltonian formalism.(Wiley, 2000) Muñoz Masqué, Jaime; Pozo Coronado, Luis MiguelThe deparametrization problem for parameter-invariant Lagrangian densities defined over J(1)(N, F), is solved in terms of a projection onto a suitable jet bundle. The Hamilton-Cartan formalism for such Lagrangians is then introduced and the pre-symplectic structure of such Variational problems is proved to be project able through the aforementioned projection. Specific examples with physical meaning are also analyzed. 1998 PACS codes. 02.20.Tw Infinite-dimensional Lie groups, 02.30.Wd Calculus of variations and optimal control, 02.40.Ky Riemannian,geometries, 02.40.Ma Global differential geometry, 02.40.Vh Global analysis and analysis on manifolds, 04.20.Fy Canonical formalism, Lagrangians, and variational principles, 11.10.Ef Lagrangian and Hamiltonian approach, 11.10.Kk Field theories in dimensions other than four, 11.25.Sq Nonperturbative techniques; string field theory. 1991 Mathematics Subject Classification. Primary: 58E30 Variational principles; Secondary: 53B20 Local Riemannian geometry, 58A20 Jets, 58E12 Applications to minimal surfaces (problems in two independent variables), 58G35 Invariance and symmetry properties, 81S10 Geometric quantization, symplectic methods, 83E30 String and superstring theories.
- PublicationClassification of Lagrangians for surface design.(Pergamon-Elsevier Science Ltd, 2001) Muñoz Masqué, Jaime; Pozo Coronado, Luis MiguelSecond-order Lagrangians depending on a surface which are parameter-invariant and also invariant under rigid motions of Euclidean 3-space are classified.
- PublicationUnrolling and rolling of curves in non-convex surfaces.(Iop science, 1999) Muñoz Masqué, Jaime; Pozo Coronado, Luis MiguelThe notion of unrolling of a spherical curve is proved to coincide with its development into the tangent plane. The development of a curve in an arbitrary surface in the Euclidean 3-space is then studied from the point of view of unrolling. The inverse operation, called the rolling of a curve onto a surface, is also analysed and the relationship of such notions with the functional defined by the square of curvature is stated. An application to the construction of nonlinear splines on Riemannian surfaces is suggested.
- PublicationParameter-invariant second-order variational problems in one variable(Iop science, 1998) Muñoz Masqué, Jaime; Pozo Coronado, Luis MiguelA projection is defined such that a second-order Lagrangian density factors through this projection module contact forms if and only if it is parameter invariant. In this way, a geometric interpretation of the parameter invariance conditions is obtained. The above projection is then used to prove the strict factorization of the Poincare-Cartan form attached to a parameter-invariant variational problem thus leading us to state the Hamilton-Cartan formalism, the complete description of symmetries and regularity for such problems. The case of the squared curvature Lagrangian in the plane is analysed especially.