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Canonoid and Poissonoid transformations, symmetries and biHamiltonian structures
Invariant metrics on Lie groups
| 1. | The University of Toledo, 2801 W Bancroft St., Toledo, OH 43606 |
References:
| [1] |
M. Anderson, A survey of Einstein Metrics on 4-Dimensional Manifolds, Handbook of Geometric Analysis, 3, International Press, Boston, 2010. |
| [2] |
T. Arias-Marco and O. Kowalski, Classification of 4-dimensional homogeneous weakly Einstein manifolds, Czechoslovak Math. J., 65 (2015), 21-59.
doi: 10.1007/s10587-015-0159-4. |
| [3] |
A. Besse, Einstein Manifolds, 1st ed., Springer, Berlin, Heidelberg, New York, 1987.
doi: 10.1007/978-3-540-74311-8. |
| [4] |
S. Chen and K. Liang, Left-invariant pseudo-Einstein metrics on Lie groups, J. Nonlinear Math. Phys., 19 (2012), 1250015, 11pp.
doi: 10.1142/S1402925112500155. |
| [5] |
Z. Chen, D. Hou and C. Bai, A left-symmetric algebraic approach to left invariant flat pseudo-metrics on Lie groups, J. Geom. Phys., 62 (2012), 1600-1610.
doi: 10.1016/j.geomphys.2012.03.003. |
| [6] |
P. Gadea, J. González-Dávila and J. Oubina, Cyclic metric Lie groups, Monatsh. Math., 176 (2015), 219-239.
doi: 10.1007/s00605-014-0692-5. |
| [7] |
M. Guediri, Novikov algebras carrying an invariant Lorentzian symmetric bilinear form, J. Geom. Phys., 82 (2014), 132-144.
doi: 10.1016/j.geomphys.2014.04.007. |
| [8] |
F. Hindeleh and G. Thompson, Killing's equations for invariant metrics on Lie groups, Journal of Geometry and Mechanics, 3 (2011), 323-335.
doi: 10.3934/jgm.2011.3.323. |
| [9] |
H. Kodama, A. Takahara and H. Tamaru, The space of left-invariant metrics on a Lie group up to isometry and scaling, Manuscripta Math., 135 (2011), 229-243.
doi: 10.1007/s00229-010-0419-4. |
| [10] |
J. Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math., 21 (1976), 293-329.
doi: 10.1016/S0001-8708(76)80002-3. |
| [11] |
J. Patera, R. T. Sharp, P. Winternitz and H. Zassenhaus, Invariants of real low dimension Lie algebras, J. Math. Phys., 17 (1976), 986-994.
doi: 10.1063/1.522992. |
| [12] |
H. Wang and S. Deng, Left invariant Einstein-Randers metrics on compact Lie groups, Canad. Math. Bull., 55 (2012), 870-881.
doi: 10.4153/CMB-2011-145-6. |
show all references
References:
| [1] |
M. Anderson, A survey of Einstein Metrics on 4-Dimensional Manifolds, Handbook of Geometric Analysis, 3, International Press, Boston, 2010. |
| [2] |
T. Arias-Marco and O. Kowalski, Classification of 4-dimensional homogeneous weakly Einstein manifolds, Czechoslovak Math. J., 65 (2015), 21-59.
doi: 10.1007/s10587-015-0159-4. |
| [3] |
A. Besse, Einstein Manifolds, 1st ed., Springer, Berlin, Heidelberg, New York, 1987.
doi: 10.1007/978-3-540-74311-8. |
| [4] |
S. Chen and K. Liang, Left-invariant pseudo-Einstein metrics on Lie groups, J. Nonlinear Math. Phys., 19 (2012), 1250015, 11pp.
doi: 10.1142/S1402925112500155. |
| [5] |
Z. Chen, D. Hou and C. Bai, A left-symmetric algebraic approach to left invariant flat pseudo-metrics on Lie groups, J. Geom. Phys., 62 (2012), 1600-1610.
doi: 10.1016/j.geomphys.2012.03.003. |
| [6] |
P. Gadea, J. González-Dávila and J. Oubina, Cyclic metric Lie groups, Monatsh. Math., 176 (2015), 219-239.
doi: 10.1007/s00605-014-0692-5. |
| [7] |
M. Guediri, Novikov algebras carrying an invariant Lorentzian symmetric bilinear form, J. Geom. Phys., 82 (2014), 132-144.
doi: 10.1016/j.geomphys.2014.04.007. |
| [8] |
F. Hindeleh and G. Thompson, Killing's equations for invariant metrics on Lie groups, Journal of Geometry and Mechanics, 3 (2011), 323-335.
doi: 10.3934/jgm.2011.3.323. |
| [9] |
H. Kodama, A. Takahara and H. Tamaru, The space of left-invariant metrics on a Lie group up to isometry and scaling, Manuscripta Math., 135 (2011), 229-243.
doi: 10.1007/s00229-010-0419-4. |
| [10] |
J. Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math., 21 (1976), 293-329.
doi: 10.1016/S0001-8708(76)80002-3. |
| [11] |
J. Patera, R. T. Sharp, P. Winternitz and H. Zassenhaus, Invariants of real low dimension Lie algebras, J. Math. Phys., 17 (1976), 986-994.
doi: 10.1063/1.522992. |
| [12] |
H. Wang and S. Deng, Left invariant Einstein-Randers metrics on compact Lie groups, Canad. Math. Bull., 55 (2012), 870-881.
doi: 10.4153/CMB-2011-145-6. |
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