Biharmonic and Interpolating Sesqui-Harmonic Vector Fields with Respect to the varphi-Sasakian Metric
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.
Keywords
Cite
@article{arxiv.2601.10216,
title = {Biharmonic and Interpolating Sesqui-Harmonic Vector Fields with Respect to the varphi-Sasakian Metric},
author = {Abderrahim Zagane and Kheireddine Biroud and Medjahed Djilali},
journal= {arXiv preprint arXiv:2601.10216},
year = {2026}
}