Isometry groups of six-dimensional filiform nilmanifolds

Document Type : Ischia Group Theory 2020/2021

Authors

1 Institute of Mathematics, University of Debrecen, Debrecen, Hungary

2 Doctoral School of Mathematical and Computational Sciences, University of Debrecen, H-4002 Debrecen, P.O.Box 400, Debrecen, Hungary

Abstract

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.

Keywords

Main Subjects


[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.
Volume 12, Issue 2 - Serial Number 2
Proceedings of the Ischia Group Theory (2020/2021) - Part 2
June 2023
Pages 67-80
  • Receive Date: 15 December 2021
  • Revise Date: 17 February 2022
  • Accept Date: 26 February 2022
  • Published Online: 01 June 2023