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http://dx.doi.org/10.5831/HMJ.2016.38.2.359

CURVATURES ON THE ABBENA-THURSTON MANIFOLD  

Han, Ju-Wan (Department of Applied Mathematics, Pukyong National University)
Kim, Hyun Woong (Department of Applied Mathematics, Pukyong National University)
Pyo, Yong-Soo (Department of Applied Mathematics, Pukyong National University)
Publication Information
Honam Mathematical Journal / v.38, no.2, 2016 , pp. 359-366 More about this Journal
Abstract
Let H be the 3-dimensional Heisenberg group, ($G=H{\times}S^1$, g) a product Riemannian manifold of Riemannian manifolds H and S with arbitrarily given left invariant Riemannian metrics respectively, and ${\Gamma}$ the discrete subgroup of G with integer entries. Then, on the Riemannian manifold ($M:=G/{\Gamma}$, ${\Pi}^*g=\bar{g}$), ${\Pi}:G{\rightarrow}G/{\Gamma}$, we evaluate the scalar curvature and the Ricci curvature.
Keywords
Heisenberg group; Abbena-Thurston manifold; scalar curvature; homogeneous Riemannian manifold; Ricci curvature;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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