Harmonicity of vector fields on the oscillator groups with neutral signature |
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Institution: | School of Mathematics and Physics, Anhui University of Technology, Maanshan, 243032, People''s Republic of China |
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Abstract: | In this paper, we mainly investigate curvature properties and harmonicity of invariant vector fields on the four-dimensional Oscillator groups endowed with three left-invariant pseudo-Riemannian metrics of signature (2,2). We determine all harmonic vector fields, vector fields which define harmonic maps and the vector fields which are critical points for the energy functional restricted to vector fields of the same length. |
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Keywords: | Harmonic vector fields Harmonic maps Oscillator group |
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