Sectional and Ricci Curvature for Three-Dimensional Lie Groups
Formulas for the Riemann and Ricci curvature tensors of an invariant metric on a Lie group are determined. The results are applied to a systematic study of the curvature properties of invariant metrics on three-dimensional Lie groups. In each case the metric is reduced by using the automorphism grou...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2016/3681529 |
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| _version_ | 1832564256972734464 |
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| author | Gerard Thompson Giriraj Bhattarai |
| author_facet | Gerard Thompson Giriraj Bhattarai |
| author_sort | Gerard Thompson |
| collection | DOAJ |
| description | Formulas for the Riemann and Ricci curvature tensors of an invariant metric on a Lie group are determined. The results are applied to a systematic study of the curvature properties of invariant metrics on three-dimensional Lie groups. In each case the metric is reduced by using the automorphism group of the associated Lie algebra. In particular, the maximum and minimum values of the sectional curvature function are determined. |
| format | Article |
| id | doaj-art-4cc31985be2b477cb2c2418535e9fcf0 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4cc31985be2b477cb2c2418535e9fcf02025-02-03T01:11:29ZengWileyJournal of Mathematics2314-46292314-47852016-01-01201610.1155/2016/36815293681529Sectional and Ricci Curvature for Three-Dimensional Lie GroupsGerard Thompson0Giriraj Bhattarai1Department of Mathematics, The University of Toledo, Toledo, OH 43606, USABristol Community College, Fall River, MA 02720, USAFormulas for the Riemann and Ricci curvature tensors of an invariant metric on a Lie group are determined. The results are applied to a systematic study of the curvature properties of invariant metrics on three-dimensional Lie groups. In each case the metric is reduced by using the automorphism group of the associated Lie algebra. In particular, the maximum and minimum values of the sectional curvature function are determined.http://dx.doi.org/10.1155/2016/3681529 |
| spellingShingle | Gerard Thompson Giriraj Bhattarai Sectional and Ricci Curvature for Three-Dimensional Lie Groups Journal of Mathematics |
| title | Sectional and Ricci Curvature for Three-Dimensional Lie Groups |
| title_full | Sectional and Ricci Curvature for Three-Dimensional Lie Groups |
| title_fullStr | Sectional and Ricci Curvature for Three-Dimensional Lie Groups |
| title_full_unstemmed | Sectional and Ricci Curvature for Three-Dimensional Lie Groups |
| title_short | Sectional and Ricci Curvature for Three-Dimensional Lie Groups |
| title_sort | sectional and ricci curvature for three dimensional lie groups |
| url | http://dx.doi.org/10.1155/2016/3681529 |
| work_keys_str_mv | AT gerardthompson sectionalandriccicurvatureforthreedimensionalliegroups AT girirajbhattarai sectionalandriccicurvatureforthreedimensionalliegroups |