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초록· 키워드
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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.
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참고문헌 (9)
참고문헌 신청
E. Abbena / 1984 / An example of an almost Kaehler manifold which is not Kaehlerian / Bollettino U.M.I 3-A:383~392
S. Helgason / 1978 / Differential Geometry, Lie Groups and Symmetric Spaces / Academic Press
S. Kobayashi / 1963 / Foundations of Differential Geometry, Vol. I / Wiley-Interscience
J. Milnor / 1976 / Curvatures of left invariant metric on Lie groups / Advances in Math 21:293~329
J.-S. Park / 1996 / The Abbena-Thurston manifold as a critical point / Canad. Math. Bull 39:352~359
S. Helgason / 1978 / Differential Geometry, Lie Groups and Symmetric Spaces / Academic Press
S. Kobayashi / 1963 / Foundations of Differential Geometry, Vol. I / Wiley-Interscience
J. Milnor / 1976 / Curvatures of left invariant metric on Lie groups / Advances in Math 21:293~329
J.-S. Park / 1996 / The Abbena-Thurston manifold as a critical point / Canad. Math. Bull 39:352~359
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