相关论文: Weingarten and Linear Weingarten Canal Surfaces

We study (2,2) divisors in $P^2 \times P^2$ giving rise to pairs of non-isomorphic, derived equivalent and L-equivalent K3 surfaces of degree 2. In particular, we confirm the existence of such fourfolds as predicted by Kuznetsov and Shinder…

We consider symmetries of K3 manifolds. Holomorphic symplectic automorphisms of K3 surfaces have been classified, and observed to be subgroups of the Mathieu group $M_{23}$. More recently, automorphisms of K3 sigma models commuting with…

In this paper we study the automorphisms group of some K3 surfaces which are double covers of the projective plane ramified over a smooth sextic plane curve. More precisely, we study some particlar case of a K3 surface of Picard rank two.

In this paper, we investigate Mannheim pairs, Frenet-Mannheim curves and Weakened Mannheim curves with respect to the modified orthogonal frame in Euclidean 3-space(E 3 ). We obtain some characterizations of these curves.

We study the geometric quantization on $K3$ surfaces from the viewpoint of the spectral convergence. We take a special Lagrangian fibrations on the $K3$ surfaces and a family of hyper-K\"ahler structures tending to large complex structure…

In this paper, we study the prescribed $k$-th Weingarten curvature problem for convex capillary hypersurfaces in $\overline{\mathbb{R}^{n+1}_+}$. This problem naturally extends the prescribed $k$-th Weingarten curvature problem for closed…

In this paper we show that there is a correspondence between some $K3$ surfaces with non-isometric transcendental lattices constructed as a twist of the transcendental lattice of the Jacobian of a generic genus 2 curve. Moreover, we show…

A marked strongly invertible knot is a triple $(K,h,\delta)$ of a knot $K$ in $S^3$, a strong inversion $h$ of $K$, and a subarc $\delta \subset \operatorname{Fix}(h)\cong S^1$ bounded by $\operatorname{Fix}(h)\cap K\cong S^0$. An invariant…

Weingarten transformations which, by definition, preserve the asymptotic lines on smooth surfaces have been studied extensively in classical differential geometry and also play an important role in connection with the modern geometric…

We review recent developments in the arithmetic of K3 surfaces. Our focus lies on aspects of modularity, Picard number and rational points. Throughout we emphasise connections to geometry.

We consider a general primitively polarized K3 surface $(S,H)$ of genus $g+1$ and a 1-nodal curve $\widetilde C\in |H|$. We prove that the normalization $C$ of $\widetilde C$ has surjective Wahl map provided $g=40,42$ or $\ge 44$.

In this paper, we study factorable surfaces in a 3-dimensional isotropic space. We classify such surfaces with constant isotropic Gaussian (K) and mean curvature (H). We provide a non-existence result related with the surfaces satisfying…

We derive basic differential geometric formulae for surfaces in hyperbolic space represented as envelopes of horospheres. The dual notion of parallel hypersurfaces is also studied. The representation is applied to prove existence and…

It is still a challenging task of today to recognize the type of a given algebraic surface which is described only by its implicit representation. In~this paper we will investigate in more detail the case of canal surfaces that are often…

We classify the Teichm\"uller curves in the moduli space of genus three Riemann surfaces $\mathcal M_3$ that are obtained by a covering construction from a primitive Teichm\"uller curve in $\mathcal M_2$. We describe the action on homology…

In this article, we study complete surfaces $\Sigma$, isometrically immersed in the product space $\mathbb{H}^2\times\mathbb{R}$ or $\mathbb{S}^2\times\mathbb{R}$ having positive extrinsic curvature $K_e$. Let $K_i$ denote the intrinsic…

We present a Bianchi-Calo type construction method for Bryant type linear Weingarten surfaces in hyperbolic space.

We find upper bounds, sharp in most cases, on the number of real hyperplane sections of real smooth polarized $K3$-surfaces that split into lines. Most bounds coincide with their complex counterparts.

In the present paper we classify curves and surfaces in Euclidean $3-$space which make constant angle with a certain Killing vector field. Moreover, we characterize the catenoid and Dini's surface in terms of constant angle surfaces.

Higher dimensional generalizations of Schwarz's $P$-surface, Schwarz's $D$-surface and Scherk's second surface are constructed as complete embedded periodic minimal hy- persurfaces in $\mathbb R^n$.