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- Title
Twisted Sasaki metric on the unit tangent bundle and harmonicity.
- Authors
LOTARETS, Liana
- 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.
- Subjects
TANGENT bundles; VECTOR fields; HARMONIC maps; LIE groups; VECTOR data; RIEMANNIAN manifolds
- Publication
Turkish Journal of Mathematics, 2024, Vol 48, Issue 2, p123
- ISSN
1300-0098
- Publication type
Article
- DOI
10.55730/1300-0098.3498