INOGUCHI Jun-ichi, NAITOH Hiroo,
Grassmann geometry on the 3-dimensional unimodular Lie groups I.
Hokkaido Mathematical Journal, 38 (2009) pp.427-496
We study the Grassmann geometry of surfaces when the ambient space is a $3$-dimensional unimodular Lie group with left invariant metric, that is, it is one of the $3$-dimensional commutative Lie group, the $3$-dimensional Heisenberg group, the groups of rigid motions on the Euclidean or the Minkowski planes, the special unitary group $SU(2)$, and the special real linear group $SL(2,\mathbb R)$.
|Uncontrolled Keywords||Grassmann geometry, unimodular Lie group, Heisenberg group, Euclidean plane, Minkowski plane, special unitary group, special linear group, totally geodesic surface, flat surface, minimal surface, surface of constant mean curvature|