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pro vyhledávání: '"Oniciuc, C."'
In this paper we shall assume that the ambient manifold is a pseudo-Riemannian space form $N^{m+1}_t(c)$ of dimension $m+1$ and index $t$ ($m\geq2$ and $1 \leq t\leq m$). We shall study hypersurfaces $M^{m}_{t'}$ which are polyharmonic of order $r$ (
Externí odkaz:
http://arxiv.org/abs/2106.07888
In this paper we shall assume that the ambient manifold is a space form $N^{m+1}(c)$ and we shall consider polyharmonic hypersurfaces of order $r$ (briefly, $r$-harmonic), where $r\geq 3$ is an integer. For this class of hypersurfaces we shall prove
Externí odkaz:
http://arxiv.org/abs/1912.10790
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 has been thoroughly studied. We shall focus on this p
Externí odkaz:
http://arxiv.org/abs/1902.01621
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 February 2023 518(1)
Publikováno v:
In Advances in Mathematics 26 August 2020 370
In this work we obtain some geometric properties of biconservative surfaces into a Riemannian manifold. In particular, we shall study the relationship between biconservative surfaces and the holomorphicity of a generalized Hopf function. Also, we giv
Externí odkaz:
http://arxiv.org/abs/1406.6774
Autor:
Loubeau, E., Oniciuc, C.
CMC surfaces in spheres are investigated under the extra condition of biharmonicity. From the work of Miyata, especially in the flat case, we give a complete description of such immersions and show that for any $h\in (0,1)$ there exist CMC proper-bih
Externí odkaz:
http://arxiv.org/abs/1403.1703
Autor:
Loubeau, E., Oniciuc, C.
Publikováno v:
Pacific J. Math. 271 (2014) 213-230
We compute a Simons' type formula for the stress-energy tensor of biharmonic maps from surfaces. Specializing to Riemannian immersions, we prove several rigidity results for biharmonic CMC surfaces, putting in evidence the influence of the Gaussian c
Externí odkaz:
http://arxiv.org/abs/1305.7020
We introduce the notion of biconservative hypersurfaces, that is hypersurfaces with conservative stress-energy tensor with respect to the bienergy. We give the (local) classification of biconservative surfaces in 3-dimensional space forms.
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Externí odkaz:
http://arxiv.org/abs/1204.1484
We prove some new rigidity results for proper biharmonic immersions in ${\mathbb S}^n$ of the following types: Dupin hypersurfaces; hypersurfaces, both compact and non-compact, with bounded norm of the second fundamental form; hypersurfaces satisfyin
Externí odkaz:
http://arxiv.org/abs/1111.6063