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RISS 인기검색어
- 검색키워드
- 저자 : Lakrini, Ibrahim (검색결과 2 건)
- 무료
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ON THE GEOMETRY OF VECTOR BUNDLES WITH FLAT CONNECTIONS
Abbassi, Mohamed Tahar Kadaoui,Lakrini, Ibrahim Korean Mathematical Society 2019 대한수학회보 Vol.56 No.5
Let $E{\rightarrow}M$ be an arbitrary vector bundle of rank k over a Riemannian manifold M equipped with a fiber metric and a compatible connection $D^E$. R. Albuquerque constructed a general class of (two-weights) spherically symmetric metrics on E. In this paper, we give a characterization of locally symmetric spherically symmetric metrics on E in the case when $D^E$ is flat. We study also the Einstein property on E proving, among other results, that if $k{\geq}2$ and the base manifold is Einstein with positive constant scalar curvature, then there is a 1-parameter family of Einstein spherically symmetric metrics on E, which are not Ricci-flat.
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On the geometry of vector bundles with flat connections
Mohamed Tahar Kadaoui Abbassi,Ibrahim Lakrini 대한수학회 2019 대한수학회보 Vol.56 No.5
Let $E \rightarrow M$ be an arbitrary vector bundle of rank $k$ over a Riemannian manifold $M$ equipped with a fiber metric and a compatible connection $D^{E}$. R.~Albuquerque constructed a general class of (two-weights) spherically symmetric metrics on $E$. In this paper, we give a characterization of locally symmetric spherically symmetric metrics on $E$ in the case when $D^E$ is flat. We study also the Einstein property on $E$ proving, among other results, that if $k \geq 2$ and the base manifold is Einstein with positive constant scalar curvature, then there is a 1-parameter family of Einstein spherically symmetric metrics on $E$, which are not Ricci-flat.
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