Hokkaido Mathematical Journal

INOGUCHI Jun-ichi, KUWABARA Kenji, NAITOH Hiroo,

Grassmann geometry on the 3-dimensional Heisenberg group.

Hokkaido Mathematical Journal, 34 (2005) pp.375-391

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Abstract

In this paper the geometries of surfaces in the 3-dimensional Heisenberg group with a left invariant metric are classified from a stand point of the Grassmann geometry, and for each of them the existence or nonexistence of surfaces with constant mean curvature is clarified.

MSC(Primary)53C40
MSC(Secondary)53B25, 53C30
Uncontrolled KeywordsHeisenberg group, Grassmann geometry of surfaces, constant mean curvature