The harmonic map flow and the Eells-Sampson theorem
Given a trajectory of a physical system, the energy of the system, more precisely the energy of the trajectory of the system, plays a central role in theoretical physics that, for example, can be used to deduce the dynamics of the system. In analogy, given a map between Riemannian manifolds, we defi...
- Autores:
-
Córdoba López, Rafael Felipe
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2021
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/53468
- Acceso en línea:
- http://hdl.handle.net/1992/53468
- Palabra clave:
- Variedades de Riemann
Teoría homotópica
Matemáticas
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-sa/4.0/
| Summary: | Given a trajectory of a physical system, the energy of the system, more precisely the energy of the trajectory of the system, plays a central role in theoretical physics that, for example, can be used to deduce the dynamics of the system. In analogy, given a map between Riemannian manifolds, we define an energy functional, in the sense of Eells and Sampson (that can be thought to be as a generalization of the physical energy), to deduce information on the target manifold. Particularly, we find that minimal curves with respect to the energy functional are, in fact, geodesics. We also introduce geometrical analysis results that allows us to probe the Eells and Sampson theorem which, in turn, can be applied for maps between pseudo-Riemannian manifolds. |
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