Biharmonic submanifolds in spheres

Caddeo, Renzo Ilario; Montaldo, Stefano; Oniciuc, Cezar

doi:10.1007/bf02764073

Cited by 197 publications

(215 citation statements)

References 5 publications

Supporting

Mentioning

204

Contrasting

Unclassified

Order By: Relevance

“…Thus,f satisfies a polynomial equation with constant coefficients, sof has to be a constant and then, f is a constant, i.e., grad f = 0 on U (in fact, f has to be zero). Therefore, we have a contradiction (see [6,8] for c = 0 and [3,4], for c = ±1).…”

mentioning

confidence: 97%

Global Properties of Biconservative Surfaces in $\mathbb{R}^3$ and $\mathbb{S}^3$

Oniciuc¹,

Nistor²

2017

Proceedings Book of International Workshop on Theory of Submanifolds

View full text Add to dashboard Cite

show abstract

mentioning

confidence: 97%

Global Properties of Biconservative Surfaces in $\mathbb{R}^3$ and $\mathbb{S}^3$

Oniciuc¹,

Nistor²

2017

Proceedings Book of International Workshop on Theory of Submanifolds

View full text Add to dashboard Cite

show abstract

“…Biharmonic submanifolds have been studied by many geometers. For example, see [2], [3], [7], [8], [11], [12], [13], [14], [15], [18], [20], [21], [22], and the references therein. In a different setting, in [9], Chen defined a biharmonic submanifold M ⊂ E n of the Euclidean space as its mean curvature vector field H satisfies ∆H = 0 , where ∆ is the Laplacian.…”

Section: Let (M G) and (N H) Be 2 Riemannian Manifolds And F : (M mentioning

confidence: 99%

On Biharmonic Legendre curves in $S$-space forms

Özgür

Güvenç²

2014

Turk J Math

View full text Add to dashboard Cite

show abstract

“…Further, all proper-biharmonic curves in S n were determined (see [18]). It was proved that, up to a totally geodesic embedding, these are the properbiharmonic curves of S 3 .…”

Section: Surface Is Proper-biharmonic In S 3 If and Only If It Is An mentioning

confidence: 99%

Harmonic and Biharmonic Maps at Iaşi

Balmus¹,

Fetcu²,

Oniciuc³

2010

Annals of the Alexandru Ioan Cuza University - Mathematics

Self Cite

View full text Add to dashboard Cite

Abstract. We report on the achievements of the geometers from Iaşi in the field of harmonic and biharmonic maps.Mathematics Subject Classification 2000: 53C07, 53C40, 53C42, 53C43, 58E20. Key words: harmonic and biharmonic maps, minimal and biharmonic submanifolds.Nowadays, the theory of harmonic maps between Riemannian manifolds is a very important field of Riemannian geometry. The harmonic maps ϕ : (M, g) → (N, h) are critical points of the energy functional E which is defined on the infinit dimensional manifold of the smooth maps from M to N ,Here dϕ is the differential of the map ϕ and ∥·∥ denotes the Hilbert-Schmidt norm. The Euler-Lagrange equation associated to the energy E is given by the vanishing of the tension field τ (ϕ) = trace ∇dϕ and it is a second order elliptic equation, as one can see from its local expressionwhere Γ denotes the Christoffel symbols and ∆ is the Laplacian acting on functions. From here raises the deep link established by the harmonic maps *

show abstract

Biharmonic submanifolds in spheres

Cited by 197 publications

References 5 publications

Global Properties of Biconservative Surfaces in $\mathbb{R}^3$ and $\mathbb{S}^3$

Global Properties of Biconservative Surfaces in $\mathbb{R}^3$ and $\mathbb{S}^3$

On Biharmonic Legendre curves in $S$-space forms

Harmonic and Biharmonic Maps at Iaşi

Contact Info

Product

Resources

About