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Turkish Journal of Mathematics

Abstract

The paper deals with the twisted Sasaki metric on the unit tangent bundle of n–dimensional Riemannian manifold Mn . The main purpose of the research is to find deformations that preserve the existence harmonic left-invariant unit vector fields on 3-dimensional unimodular Lie groups G with the left invariant metric and harmonic maps G → T1G in case of twisted Sasaki metric on the unit tangent bundle. The necessary and sufficient conditions for harmonicity of left-invariant unit vector field and map Mn → T1Mn are obtained. The necessary and sufficient conditions for harmonicity of left-invariant unit vector field and map M2 → T1M2 with respect to some orthonormal frame are obtained. Left-invariant harmonic unit vector fields and harmonic maps G → T1G, where G is a three-dimensional unimodular Lie group with left-invariant metric, using some orthonormal frame are described. Left-invariant harmonic unit vector fields which determine harmonic maps G → T1G, where G is a three-dimensional unimodular Lie group with left-invariant metric in the particular case of twisted Sasaki metric, namely the vertical rescaled metric are classified.

DOI

10.55730/1300-0098.3498

Keywords

harmonic map, harmonic vector field, Lie group, Twisted Sasaki metric, unit tangent bundle, vertical rescaled metric

First Page

123

Last Page

143

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