Finsler metrics with propierties of the Kobayashi metric on convex domains.

Pang, Myung-Yull. "Finsler metrics with propierties of the Kobayashi metric on convex domains.." Publicacions Matemàtiques 36.1 (1992): 131-155. <http://eudml.org/doc/41163>.

@article{Pang1992,
abstract = {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.},
author = {Pang, Myung-Yull},
journal = {Publicacions Matemàtiques},
keywords = {Métrica; Dominios convexos; Foliaciones; Variedades complejas; totally geodesic complex curve; extremal disks},
language = {eng},
number = {1},
pages = {131-155},
title = {Finsler metrics with propierties of the Kobayashi metric on convex domains.},
url = {http://eudml.org/doc/41163},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Pang, Myung-Yull
TI - Finsler metrics with propierties of the Kobayashi metric on convex domains.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 1
SP - 131
EP - 155
AB - 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.
LA - eng
KW - Métrica; Dominios convexos; Foliaciones; Variedades complejas; totally geodesic complex curve; extremal disks
UR - http://eudml.org/doc/41163
ER -