Biharmonic and biconservative hypersurfaces in space forms
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Publication:5085351
DOI10.1090/conm/777/15628zbMath1504.53077arXiv2012.12476OpenAlexW3114673367MaRDI QIDQ5085351
Dorel Fetcu, Cezar Dumitru Oniciuc
Publication date: 27 June 2022
Published in: Differential Geometry and Global Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.12476
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Rigidity results (53C24) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)
Related Items (8)
Triharmonic CMC hypersurfaces in space forms with at most \(3\) distinct principal curvatures ⋮ Biconservative surfaces in the 4-dimensional Euclidean sphere ⋮ Biharmonic conjectures on hypersurfaces in a space form ⋮ Parallel mean curvature biconservative surfaces in complex space forms ⋮ Biharmonic homogeneous polynomial maps between spheres ⋮ The energy density of biharmonic quadratic maps between spheres ⋮ A new gap for \textit{CMC} biharmonic hypersurfaces in Euclidean spheres ⋮ Closed biconservative hypersurfaces in spheres
Cites Work
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- Biconservative surfaces
- Proper biconservative immersions into the Euclidean space
- Biharmonic hypersurfaces in Riemannian symmetric spaces. I.
- Constant mean curvature proper-biharmonic surfaces of constant Gaussian curvature in spheres
- Complete biconservative surfaces in \(\mathbb{R}^3\) and \(\mathbb{S}^3\)
- Biharmonic PNMC submanifolds in spheres
- Biharmonic submanifolds with parallel mean curvature in \(\mathbb{S}^{n}\times\mathbb{R}\)
- Biharmonic integral \(\mathcal{C}\)-parallel submanifolds in 7-dimensional Sasakian space forms
- Biharmonic surfaces of constant mean curvature
- CMC biconservative surfaces in \(\mathbb S^n\times\mathbb R\) and \(\mathbb H^n\times\mathbb R\)
- Biharmonic hypersurfaces in Riemannian manifolds
- Biharmonic submanifolds with parallel mean curvature vector field in spheres
- On biconservative surfaces in 4-dimensional Euclidean space
- Biharmonic submanifolds in spheres.
- Biharmonic submanifolds of \({\mathbb{C}\mathbb{P}^n}\)
- A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order
- Unique continuation property for biharmonic hypersurfaces in spheres
- Biharmonic homogeneous hypersurfaces in compact symmetric spaces
- Tangentially biharmonic Lagrangian \(H\)-umbilical submanifolds in complex space forms
- H-hypersurfaces with three distinct principal curvatures in the Euclidean spaces
- Biharmonic surfaces with parallel mean curvature in complex space forms
- The stress-energy tensor for biharmonic maps
- Classification results for biharmonic submanifolds in spheres
- Biharmonic hypersurfaces in Sasakian space forms
- 2-type surfaces of constant curvature in \(S^n\)
- Hypersurfaces with constant scalar curvature
- A closed hypersurface with constant scalar and mean curvatures in \(\mathbb{S}^ 4\) is isoparametric
- Geometric superrigidity
- On closed hypersurfaces of constant scalar curvatures and mean curvatures in \(S^{n+1}\)
- Closed generalized elastic curves in \({\mathbf S}^{2}\)(1).
- Biharmonic hypersurfaces in Riemannian symmetric spaces. II
- Biharmonic hypersurfaces with constant scalar curvature in space forms
- Biconservative submanifolds in \(\mathbb {S}^n\times \mathbb {R}\) and \(\mathbb {H}^n\times \mathbb {R}\)
- Surfaces in Euclidean 3-space whose normal bundles are tangentially biharmonic
- Surfaces of constant mean curvature in manifolds of constant curvature
- Proper biharmonic submanifolds in a sphere
- Quasi-biharmonic Lagrangian surfaces in Lorentzian complex space forms
- Surfaces in three-dimensional space forms with divergence-free stress-bienergy tensor
- On Chen's biharmonic conjecture for hypersurfaces in \(\mathbb{R}^5\)
- Complete biconservative surfaces in the hyperbolic space \(\mathbb{H}^3\)
- Some classifications of biharmonic hypersurfaces with constant scalar curvature
- Four dimensional biharmonic hypersurfaces in nonzero space forms have constant mean curvature
- Classification theorems for biharmonic real hypersurfaces in a complex projective space
- Explicit classification of biconservative surfaces in Lorentz 3-space forms
- On biconservative surfaces in \(3\)-dimensional space forms
- On biconservative surfaces
- Classification of biharmonic \(\mathcal{C}\)-parallel Legendrian submanifolds in 7-dimensional Sasakian space forms
- A formula of Simons' type and hypersurfaces with constant mean curvature
- Bochner-Simons formulas and the rigidity of biharmonic submanifolds
- Biharmonic hypersurfaces in hemispheres
- Complete classification of biconservative hypersurfaces with diagonalizable shape operator in the Minkowski 4-space
- New results toward the classification of Biharmonic submanifolds in $\mathbb{S}^{n}$
- Total Mean Curvature and Submanifolds of Finite Type
- Biharmonic hypersurfaces with bounded mean curvature
- Biharmonic hypersurfaces in a sphere
- Biharmonic hypersurfaces in 4-dimensional space forms
- Classifications and Isolation Phenomena of Bi-Harmonic Maps and Bi-Yang-Mills Fields
- Bi-harmonic maps and bi-Yang-Mills fields
- BIHARMONIC SURFACES IN PSEUDO-EUCLIDEAN SPACES
- Biconservative surfaces in BCV‐spaces
- On the uniqueness of complete biconservative surfaces in $\mathbb {R}^3$
- On Totally Real Submanifolds
- BIHARMONIC SUBMANIFOLDS OF ${\mathbb S}^3$
- Hypersurfaces in E4 with Harmonic Mean Curvature Vector Field
- Totally biharmonic hypersurfaces in space forms and 3-dimensional BCV spaces
- Biharmonic Submanifolds and Biharmonic Maps in Riemannian Geometry
- Unique continuation theorems for biharmonic maps
- Biharmonic hypersurfaces with three distinct principal curvatures in spheres
- On biconservative hypersurfaces in ‐dimensional Riemannian space forms
- Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
- Harmonic Mappings of Riemannian Manifolds
- Biharmonic hypersurfaces in a product space Lm×R
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