Zobrazeno 1 - 10
of 166
pro vyhledávání: '"Dillen, Franki"'
It was proven in [B.-Y. Chen, F. Dillen, J. Van der Veken and L. Vrancken, Curvature inequalities for Lagrangian submanifolds: the final solution, Differ. Geom. Appl. 31 (2013), 808-819] that every Lagrangian submanifold $M$ of a complex space form $
Externí odkaz:
http://arxiv.org/abs/1705.00685
Autor:
Chen, Bang-Yen, Dillen, Franki
The famous Nash embedding theorem published in 1956 was aiming for the opportunity to use extrinsic help in the study of (intrinsic) Riemannian geometry, if Riemannian manifolds could be regarded as Riemannian submanifolds. However, this hope had not
Externí odkaz:
http://arxiv.org/abs/1307.1828
Let $M$ be an $n$-dimensional Lagrangian submanifold of a complex space form. We prove a pointwise inequality $$\delta(n_1,\ldots,n_k) \leq a(n,k,n_1,\ldots,n_k) \|H\|^2 + b(n,k,n_1,\ldots,n_k)c,$$ with on the left hand side any delta-invariant of th
Externí odkaz:
http://arxiv.org/abs/1307.1497
In this paper almost complex surfaces of the nearly K\"ahler $S^3\times S^3$ are studied in a systematic way. We show that on such a surface it is possible to define a global holomorphic differential, which is induced by an almost product structure o
Externí odkaz:
http://arxiv.org/abs/1208.0737
In this article we obtain a classification of special Lagrangian submanifolds in complex space forms subject to an $SO(2)\rtimes S_3$-symmetry on the second fundamental form. The algebraic structure of this form has been obtained by Marianty Ionel. H
Externí odkaz:
http://arxiv.org/abs/1107.0855
Autor:
Dillen, Franki, Kowalczyk, Daniel
We classify all the surfaces in $M^2(c_1)\times M^2(c_2)$ for which the tangent space $T_pM^2$ makes constant angles with $T_p(M^2(c_1)\times \{p_2\})$ (or equivalently with $T_p(\{p_1\}\times M^2(c_2))$ for every point $p=(p_1,p_2)$ of $M^2$. Here $
Externí odkaz:
http://arxiv.org/abs/1105.0813
In this article we study surfaces in $\mathbb{S}^3(1) \times \mathbb{R}$ for which the $\mathbb{R}$-direction makes a constant angle with the normal plane. We give a complete classification for such surfaces with parallel mean curvature vector.
Externí odkaz:
http://arxiv.org/abs/1105.0503
Publikováno v:
Taiwanese J. Math., 15 (2011) 5, 2265-2289
In this paper we characterize and classify surfaces in ${\mathbb{H}}^2\times{\mathbb{R}}$ which have a canonical principal direction. Here ${\mathbb{H}}^2$ denotes the hyperbolic plane. We study some geometric properties such as minimality and flatne
Externí odkaz:
http://arxiv.org/abs/0910.2135
Publikováno v:
Balkan Journal of Geometry and Its Applications, 16 (2011) 2, 35 - 47
Let $I \subseteq \R$ be an open interval, $f : I \to \R$ a strictly positive function and denote by $\E^2$ the Euclidean plane. We classify all surfaces in the warped product manifold $I \times_f \E^2$ for which the unit normal makes a constant angle
Externí odkaz:
http://arxiv.org/abs/0908.1180
Autor:
Dillen, Franki, Munteanu, Marian Ioan
Publikováno v:
Bulletin Braz. Math. Soc. 40 (2009) 1, 85 - 97
In this paper we classify constant angle surfaces in $\H^2\times\R$, where $\H^2$ is the hyperbolic plane.
Comment: 9 Latex pages
Comment: 9 Latex pages
Externí odkaz:
http://arxiv.org/abs/0705.3744