| Title:
|
Harmonic metrics on four dimensional non-reductive homogeneous manifolds (English) |
| Author:
|
Zaeim, Amirhesam |
| Author:
|
Atashpeykar, Parvane |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
2 |
| Year:
|
2018 |
| Pages:
|
475-490 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study harmonic metrics with respect to the class of invariant metrics on non-reductive homogeneous four dimensional manifolds. In particular, we consider harmonic lifted metrics with respect to the Sasaki lifts, horizontal lifts and complete lifts of the metrics under study. (English) |
| Keyword:
|
harmonic metric |
| Keyword:
|
non-reductive homogeneous space |
| Keyword:
|
pseudo-Riemannian geometry |
| MSC:
|
53C43 |
| MSC:
|
53C55 |
| idZBL:
|
Zbl 06890384 |
| idMR:
|
MR3819185 |
| DOI:
|
10.21136/CMJ.2018.0502-16 |
| . |
| Date available:
|
2018-06-11T10:55:35Z |
| Last updated:
|
2020-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147230 |
| . |
| Reference:
|
[1] Baird, P., Wood, J. C.: Harmonic Morphisms Between Riemannian Manifolds.London Mathematical Society Monographs New Series 29, Oxford University Press, Oxford (2003). Zbl 1055.53049, MR 2044031, 10.1093/acprof:oso/9780198503620.001.0001 |
| Reference:
|
[2] Bejan, C.-L., Druţă-Romaniuc, S.-L.: Connections which are harmonic with respect to general natural metrics.Differ. Geom. Appl. 30 (2012), 306-317. Zbl 1252.53083, MR 2926271, 10.1016/j.difgeo.2012.05.004 |
| Reference:
|
[3] Bejan, C.-L., Druţă-Romaniuc, S.-L.: Harmonic almost complex structures with respect to general natural metrics.Mediterr. J. Math. 11 (2014), 123-136. Zbl 1317.53041, MR 3160617, 10.1007/s00009-013-0302-0 |
| Reference:
|
[4] Bejan, C.-L., Druţă-Romaniuc, S.-L.: Structures which are harmonic with respect to Walker metrics.Mediterr. J. Math. 12 (2015), 481-496. Zbl 1322.53065, MR 3350322, 10.1007/s00009-014-0409-y |
| Reference:
|
[5] Benyounes, M., Loubeau, E., Wood, C. M.: Harmonic sections of Riemannian vector bundles, and metrics of Cheeger-Gromoll type.Differ. Geom. Appl. 25 (2007), 322-334. Zbl 1128.53037, MR 2330461, 10.1016/j.difgeo.2006.11.010 |
| Reference:
|
[6] Brozos-Vázquez, M., García-Río, E., Gilkey, P., Nikčević, S., Vázquez-Lorenzo, R.: The Geometry of Walker Manifolds.Synthesis Lectures on Mathematics and Statistics 5, Morgan & Claypool Publishers, San Rafael (2009). Zbl 1206.53039, MR 2656431, 10.2200/S00197ED1V01Y200906MAS005 |
| Reference:
|
[7] Calvaruso, G., Fino, A.: Ricci solitons and geometry of four-dimensional non-reductive homogeneous spaces.Can. J. Math. 64 (2012), 778-804. Zbl 1252.53056, MR 2957230, 10.4153/CJM-2011-091-1 |
| Reference:
|
[8] Calvaruso, G., Fino, A., Zaeim, A.: Homogeneous geodesics of non-reductive homogeneous pseudo-Riemannian 4-manifolds.Bull. Braz. Math. Soc. (N.S.) 46 (2015), 23-64. Zbl 1318.53048, MR 3324177, 10.1007/s00574-015-0083-0 |
| Reference:
|
[9] Calvaruso, G., Zaeim, A.: A complete classification of Ricci and Yamabe solitons of non-reductive homogeneous 4-spaces.J. Geom. Phys. 80 (2014), 15-25. Zbl 1286.53046, MR 3188790, 10.1016/j.geomphys.2014.02.007 |
| Reference:
|
[10] Calvaruso, G., Zaeim, A.: Geometric structures over non-reductive homogeneous 4-spaces.Adv. Geom. 14 (2014), 191-214. Zbl 1298.53072, MR 3263422, 10.1515/advgeom-2014-0014 |
| Reference:
|
[11] Chen, B.-Y., Nagano, T.: Harmonic metrics, harmonic tensors, and Gauss maps.J. Math. Soc. Japan 36 (1984), 295-313. Zbl 0543.58015, MR 0740319, 10.2969/jmsj/03620295 |
| Reference:
|
[12] Dodson, C. T. J., Pérez, M. Trinidad, Vázquez-Abal, M. E.: Harmonic-Killing vector fields.Bull. Belg. Math. Soc. Simon Stevin 9 (2002), 481-490. Zbl 1044.53052, MR 2016229, 10.36045/bbms/1102714982 |
| Reference:
|
[13] J. Eells, Jr., J. H. Sampson: Harmonic mappings of Riemannian manifolds.Am. J. Math. 86 (1964), 109-160. Zbl 0122.40102, MR 0164306, 10.2307/2373037 |
| Reference:
|
[14] Falcitelli, M., Pastore, A. M.: On the tangent bundle and on the bundle of the linear frames over an affinely connected manifold.Math. Balk., New Ser. 2 (1988), 336-356. Zbl 0677.53040, MR 0997625 |
| Reference:
|
[15] Fels, M. E., Renner, A. G.: Non-reductive homogeneous pseudo-Riemannian manifolds of dimension four.Can. J. Math. 58 (2006), 282-311. Zbl 1100.53043, MR 2209280, 10.4153/CJM-2006-012-1 |
| Reference:
|
[16] Kowalski, O., Sekizawa, M.: Almost Osserman structures on natural Riemann extensions.Differ. Geom. Appl. 31 (2013), 140-149. Zbl 1277.53016, MR 3010084, 10.1016/j.difgeo.2012.10.007 |
| Reference:
|
[17] O'Neill, B.: Semi-Riemannian Geometry. With Applications to Relativity.Pure and Applied Mathematics 103, Academic Press, New York (1983). Zbl 0531.53051, MR 0719023 |
| Reference:
|
[18] Patera, J., Sharp, R. T., Winternitz, P., Zassenhaus, H.: Invariants of real low dimension Lie algebras.J. Math. Phys. 17 (1976), 986-994. Zbl 0357.17004, MR 0404362, 10.1063/1.522992 |
| Reference:
|
[19] Yano, K., Ishihara, S.: Tangent and Cotangent Bundles. Differential Geometry.Pure and Applied Mathematics 16, Marcel Dekker, New York (1973). Zbl 0262.53024, MR 0350650 |
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