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Isometry groups of six-dimensional filiform nilmanifolds | ||
| International Journal of Group Theory | ||
| مقاله 19، دوره 12، شماره 2، شهریور 2023، صفحه 67-80 اصل مقاله (402.54 K) | ||
| نوع مقاله: Ischia Group Theory 2020/2021 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2022.131891.1767 | ||
| نویسندگان | ||
| Agota Figula* 1؛ Sameer Annon Abbas2 | ||
| 1Institute of Mathematics, University of Debrecen, Debrecen, Hungary | ||
| 2Doctoral School of Mathematical and Computational Sciences, University of Debrecen, H-4002 Debrecen, P.O.Box 400, Debrecen, Hungary | ||
| چکیده | ||
| In this paper, we classify up to isometry the connected and simply connected Riemannian nilmanifolds on six-dimensional filiform Lie groups and we compute the corresponding isometry groups. | ||
| کلیدواژه‌ها | ||
| filiform nilpotent Lie groups؛ filiform metric Lie algebras؛ isometry groups of nilmanifolds؛ the group of orthogonal automorphisms of metric Lie algebras | ||
| مراجع | ||
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[1] G. Cairns, A. Hinić Galić and Yu. Nikolayevsky, Totally geodesic subalgebras of nilpotent Lie algebras, J. Lie Theory, 23 no. 4 (2013) 1023–1049. [2] G. Cairns, A. Hinić Galić and Yu. Nikolayevsky, Totally geodesic subalgebras of filiform nilpotent Lie algebras, J. Lie Theory, 23 no. 4 (2013) 1051–1074. [3] S. Console, A. Fino and E. Samiou, The moduli space of 6-dimensional 2-step nilpotent Lie algebras, Ann. Global Anal. Geom., 27 (2005) 17–32. [4] Á. Figula and P. T. Nagy, Isometry classes of simply connected nilmanifolds, J. Geom. Phys., 132 (2018) 370–381.
[5] W. A. de Graaf, Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2, J. Algebra, 309 no. 2 (2007) 640–653. [6] S. Homolya and O. Kowalski, Simply connected two-step homogeneous nilmanifolds of dimension 5, Note Mat., 26 no. 1 (2006) 69–77. [7] M. M. Kerr and T. L. Payne, The geometry of filiform nilpotent Lie groups, Rocky Mountain J. Math., 40 no. 5 (2010) 1587–1610. [8] J. Lauret, Homogeneous nilmanifolds of dimension 3 and 4, Geom. Dedicata, 68 (1997) 145–155.
[9] E. Wilson, Isometry groups on homogeneous nilmanifolds, Geom. Dedicata, 12 (1982) 337-346. | ||
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آمار تعداد مشاهده مقاله: 557 تعداد دریافت فایل اصل مقاله: 247 |
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