CURVATURES ON THE ABBENA-THURSTON MANIFOLD

• Journal title : Honam Mathematical Journal
• Volume 38, Issue 2,  2016, pp.359-366
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2016.38.2.359
Title & Authors
CURVATURES ON THE ABBENA-THURSTON MANIFOLD
Han, Ju-Wan; Kim, Hyun Woong; Pyo, Yong-Soo;

Abstract
Let H be the 3-dimensional Heisenberg group, ($\small{G=H{\times}S^1}$, g) a product Riemannian manifold of Riemannian manifolds H and S with arbitrarily given left invariant Riemannian metrics respectively, and $\small{{\Gamma}}$ the discrete subgroup of G with integer entries. Then, on the Riemannian manifold ($\small{M:=G/{\Gamma}}$, $\small{{\Pi}^*g=\bar{g}}$), $\small{{\Pi}:G{\rightarrow}G/{\Gamma}}$, we evaluate the scalar curvature and the Ricci curvature.
Keywords
Heisenberg group;Abbena-Thurston manifold;scalar curvature;homogeneous Riemannian manifold;Ricci curvature;
Language
English
Cited by
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