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

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“…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

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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

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“…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

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“…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

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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 *

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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

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