Biharmonic and Interpolating Sesqui-Harmonic Vector Fields with Respect to the varphi-Sasakian Metric

Abderrahim Zagane; Kheireddine Biroud; Medjahed Djilali

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arXiv · 2601.10216

Biharmonic and Interpolating Sesqui-Harmonic Vector Fields with Respect to the varphi-Sasakian Metric

Abderrahim Zagane·Kheireddine Biroud·Medjahed Djilali

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Abstract

This work investigates biharmonic and interpolating sesqui-harmonic vector fields on the tangent bundle of a para-K\"ahler--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.

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Abderrahim Zagane, Kheireddine Biroud, Medjahed Djilali. 2026-01-15. Biharmonic and Interpolating Sesqui-Harmonic Vector Fields with Respect to the varphi-Sasakian Metric. https://arxiv.org/abs/2601.10216

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