Título inglés |
Finsler metrics with propierties of the Kobayashi metric on convex domains. |
Título español |
Métricas de Finsler con propiedades de la métrica de Kobayashi en dominios convexos. |
Autor/es |
Pang, Myung-Yull |
Organización |
Dep. Math. Washington Univ., Saint Louis (Missouri), Estados Unidos |
Revista |
0214-1493 |
Publicación |
1992, 36 (1): 131-155, 14 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
The structure of complex Finsler manifolds is studied when the Finsler metric has the property of the Kobayashi metric on convex domains: (real) geodesics locally extend to complex curves (extremal disks). It is shown that this property of the Finsler metric induces a complex foliation of the cotangent space closely related to geodesics. Each geodesic of the metric is then shown to have a unique extension to a maximal totally geodesic complex curve Σ which has properties of extremal disks. Under the additional conditions that the metric is complete and the holomorphic sectional curvature is -4, Σ coincides with an extremal disk and a theorem of Faran is recovered: the Finsler metric coincides with the Kobayashi metric. |
Clasificación UNESCO |
120211 ; 120404 |
Palabras clave español |
Métrica ; Dominios convexos ; Foliaciones ; Variedades complejas |
Acceso al artículo completo |