Left-Invariant Minimal Unit Vector Fields on the Solvable Lie Group

Abstract

Božek (1980) has introduced a class of solvable Lie groups G_n with arbitrary odd dimension to construct irreducible generalized symmetric Riemannian space such that the identity component of its full isometry group is solvable. In this article, the authors provide the set of all left-invariant minimal unit vector fields on the solvable Lie group G_n, and give the relationships between the minimal unit vector fields and the geodesic vector fields, the strongly normal unit vectors respectively.

Keywords

Solvable Lie groups / Lagrangian multiplier method / Minimal unit vector fields / Geodesic vector fields / Strongly normal unit vectors

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