arXiv research

Study f-biharmonic maps and submanifolds, proving rigidity and classifications.

f-Biharmonic maps are the extrema of the f-bienergy functional. f-biharmonic submanifolds are submanifolds whose defining isometric immersions are f-biharmonic maps. In this paper, we prove that an f-biharmonic map from a compact Riemannian manifold into a non-positively curved manifold with constant f-bienergy density…

Study of $f$-biharmonic hypersurfaces in conformally flat spaces.

The paper studies $f$-biharmonic maps and submersions in space forms.

Study f-biharmonic and bi-f-harmonic submanifolds in complex and Sasakian space forms.

The paper defines and analyzes $f$-biharmonic $θ_{α}$-slant curves in $\mathcal{S}$-space forms.

We study biharmonic maps and f-biharmonic maps from a round sphere $(S^2, g_0)$, the latter maps are equivalent to biharmonic maps from Riemann spheres $(S^2, f^{-1}g_0)$. We proved that for rotationally symmetric maps between rotationally symmetric spaces, both biharmonicity and f-biharmonicity reduce to a 2nd order l…

The paper shows bi-f-harmonic and f-biharmonic maps are equivalent and explores their properties.

Proves generalized Chen's conjecture for biharmonic maps on foliations.

Both bi-harmonic map and $f$-harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study $f$-bi-harmonic maps as the critical points of the $f$-bi-energy functional $\frac{1}{2}\int_M f|τ(φ)|^2dv_{g}$. This class of maps generalizes both …

The paper studies $f$-polyharmonic maps and their properties.