Soluções invariantes para o tensor de Schouten e tensor curvatura prescritos em variedades localmente conformemente planas
Nenhuma Miniatura disponível
Data
2018-06-12
Autores
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Federal de Goiás
Resumo
In this work we study two problems: the first one involving the prescribed Schouten tensor and the second one the prescribed curvature operator. The first problem was inspired by the works Deturck and Yang, [6], which consist of: Given a tensor T of order 2 in the pseudo-Euclidean space (
,g), n ≥ 3, with coordinates x = (
), and metric g, where
,
= ±1, find a metric as
=
g, such that the tensor of Schouten
be T.
The second problem is the problem of the prescribed curvature tensor consist of: Let Euclidean space (
;g), n ≥ 3, with coordinates x = (
), is
, the R a tensor of order 4 of the form
, where T =
, with
differentiable functions.We want to find a metric
=
g, such that
=
, where
is the tensor curvature of the metric
. Considering that the solutions are invariant by translation and rotation, we find necessary and sufficient conditions for both problems to have solution.
Descrição
Palavras-chave
Citação
Carvalho, M. T. A. Soluções invariantes para o tensor de Schouten e tensor curvatura prescritos em variedades localmente conformemente planas. 2018. 68 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2018.