On some geometrical properties of six-dimensional nilpotent Lie group N6,11

S.Jangir, J. Kaur, G. Shanker

In this paper, we study left invariant Randers metric F on six-dimensional nilpotent Lie group N6,11 with Lie algebra n6,11. We compute Levi-civita connection, Riemann curvature tensor, sectional curvature, Ricci curvature and scalar curvature on (N6,11, F). Moreover, we classify simply connected six-dimensional nilpotent Lie groups equipped with (α,β)-metrics of Douglas and Berwald type defined by left-invariant Riemannian metric and left-invariant vector field. We also compute S-curvature and flag curvature. At the end it is also proved that (N6,11, F) can neither be naturally reductive nor Ricci-quadratic. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 17(3) (2024), pp. 111-123