## 2 Citations

Stability and the index of biharmonic hypersurfaces in a Riemannian manifold

- MathematicsAnnali di Matematica Pura ed Applicata (1923 -)
- 2021

In this paper, we give an explicit second variation formula for a biharmonic hypersurface in a Riamannian manifold similar to that of a minimal hypersurface. We then use the second variation formula…

On p-biharmonic curves

- Mathematics, Computer Science
- 2022

By making a connection to magnetic geodesic the authors are able to prove the existence of 12 -biharmonic curves on closed surfaces and classify 12 -elastic curves onclosed surfaces and three-dimensional space forms making use of the results obtained for 12 -Elastic curves from the literature.

## References

SHOWING 1-10 OF 20 REFERENCES

Stability and the index of biharmonic hypersurfaces in a Riemannian manifold

- MathematicsAnnali di Matematica Pura ed Applicata (1923 -)
- 2021

In this paper, we give an explicit second variation formula for a biharmonic hypersurface in a Riamannian manifold similar to that of a minimal hypersurface. We then use the second variation formula…

Biharmonic Conformal Maps in Dimension Four and Equations of Yamabe-Type

- Mathematics
- 2017

We prove that the problem of constructing biharmonic conformal maps on a 4-dimensional Einstein manifold reduces to a Yamabe-type equation. This allows us to construct an infinite family of examples…

On conformal biharmonic immersions

- Mathematics
- 2008

This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension field under conformal change of metrics. We then obtain an invariant…

A General Approach to Equivariant Biharmonic Maps

- Mathematics
- 2011

In this paper we describe a 1-dimensional variational approach to the analytical construction of equivariant biharmonic maps. Our goal is to provide a direct method which enables analysts to compute…

On the biharmonic and harmonic indices of the Hopf map

- Mathematics
- 2004

Biharmonic maps are the critical points of the bienergy functional and, from this point of view, generalize harmonic maps. We consider the Hopf map and modify it into a nonharmonic biharmonic map .…

Index and nullity of proper biharmonic maps in spheres

- MathematicsCommunications in Contemporary Mathematics
- 2020

In recent years, the study of the bienergy functional has attracted the attention of a large community of researchers, but there are not many examples where the second variation of this functional…

Stability of λ-Harmonic Maps

- MathematicsMathematics
- 2018

In this paper, λ -harmonic maps from a Finsler manifold to a Riemannian manifold are studied. Then, some properties of this kind of harmonic maps are presented and some examples are given. Finally,…