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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.10216 |
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| _version_ | 1866908767635898368 |
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| author | Zagane, Abderrahim Biroud, Kheireddine Djilali, Medjahed |
| author_facet | Zagane, Abderrahim Biroud, Kheireddine Djilali, Medjahed |
| contents | This work investigates biharmonic and interpolating sesqui-harmonic vector fields on the tangent bundle of a para-Kähler--Norden manifold (M, varphi, g) endowed with the varphi-Sasaki metric. We derive the first variation of the bienergy and interpolating sesqui-energy functionals, restricted to the space of vector fields. Explicit characterizations are established for vector fields satisfying the corresponding variational conditions-namely, biharmonicity and interpolating sesqui-harmonicity. Furthermore, several examples are presented to illustrate the general theory and to elucidate the distinctions between harmonic, biharmonic, and interpolating sesqui-harmonic behaviors. These results extend and complement existing research on higher-order harmonicity in pseudo-Riemannian geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10216 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Biharmonic and Interpolating Sesqui-Harmonic Vector Fields with Respect to the varphi-Sasakian Metric Zagane, Abderrahim Biroud, Kheireddine Djilali, Medjahed Differential Geometry This work investigates biharmonic and interpolating sesqui-harmonic vector fields on the tangent bundle of a para-Kähler--Norden manifold (M, varphi, g) endowed with the varphi-Sasaki metric. We derive the first variation of the bienergy and interpolating sesqui-energy functionals, restricted to the space of vector fields. Explicit characterizations are established for vector fields satisfying the corresponding variational conditions-namely, biharmonicity and interpolating sesqui-harmonicity. Furthermore, several examples are presented to illustrate the general theory and to elucidate the distinctions between harmonic, biharmonic, and interpolating sesqui-harmonic behaviors. These results extend and complement existing research on higher-order harmonicity in pseudo-Riemannian geometry. |
| title | Biharmonic and Interpolating Sesqui-Harmonic Vector Fields with Respect to the varphi-Sasakian Metric |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2601.10216 |