Zobrazeno 1 - 10
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pro vyhledávání: '"Vrancken, Luc"'
In this paper, we classify the hypersurfaces of $\mathbb{S}^2\times\mathbb{S}^2$ with constant sectional curvature. By applying the so-called Tsinghua principle, which was first discovered by the first three authors in 2013 at Tsinghua University, we
Externí odkaz:
http://arxiv.org/abs/2302.00466
We construct an explicit map from a generic minimal $\delta(2)$-ideal Lagrangian submanifold of $\mathbb{C}^n$ to the quaternionic projective space $\mathbb{H}P^{n-1}$, whose image is either a point or a minimal totally complex surface. A stronger re
Externí odkaz:
http://arxiv.org/abs/2301.05594
Autor:
Cwilinski, Kamil, Vrancken, Luc
We study and classify almost complex totally geodesic submanifolds of the nearly Kaehler flag manifold $F_{1,2}(\mathbb C^3)$, and of its semi-Riemannian counterpart. We also develop a structural approach to the nearly Kaehler flag manifold $F_{1,2}(
Externí odkaz:
http://arxiv.org/abs/2107.00920
In this paper, through making careful analysis of Gauss and Codazzi equations, we prove that four dimensional biharmonic hypersurfaces in nonzero space form have constant mean curvature. Our result gives the positive answer to the conjecture proposed
Externí odkaz:
http://arxiv.org/abs/2007.13589
Autor:
Ghandour, Elsa, Vrancken, Luc
The space $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$ admits a natural homogeneous pseudo-Riemannian nearly Kaehler structure. We investigate almost complex surfaces in this space. In particular we obtain a complete classification of the totally geodes
Externí odkaz:
http://arxiv.org/abs/2006.11906
Publikováno v:
The Journal of Geometric Analysis, 2019
In this paper we consider minimal Lagrangian submanifolds in $n$-dimensional complex space forms. More precisely, we study such submanifolds which, endowed with the induced metrics, write as a Riemannian product of two Riemannian manifolds, each havi
Externí odkaz:
http://arxiv.org/abs/1912.05331
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Publikováno v:
Pacific J. Math. 315 (2021) 27-44
In this paper, we study locally strongly convex Tchebychev hypersurfaces, namely the {\it centroaffine totally umbilical hypersurfaces}, in the $(n+1)$-dimensional affine space $\mathbb{R}^{n+1}$. We first make an ordinary-looking observation that su
Externí odkaz:
http://arxiv.org/abs/1911.05222
Publikováno v:
SCIENCE CHINA Mathematics, 63 (2020), 2055-2078
In this paper, we study locally strongly convex affine hyperspheres in the unimodular affine space $\mathbb{R}^{n+1}$ which, as Riemannian manifolds, are locally isometric to the Riemannian product of two Riemannian manifolds both possessing constant
Externí odkaz:
http://arxiv.org/abs/1812.07901
We introduce a structural approach to study Lagrangian submanifolds of the complex hyperquadric in arbitrary dimension by using its family of non-integrable almost product structures. In particular, we define local angle functions encoding the geomet
Externí odkaz:
http://arxiv.org/abs/1812.07888