Related papers: Complete classification of biconservative hypersur…
We obtain a complete classification of proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces with arbitrary dimension. Precisely, together with known results of Balmu\c{s}-Montaldo-Oniciuc, we…
This article introduces and studies Minkowski Bisectors, Minkowski Cells, and Lattice Coverings.
In this paper, we extend our investigation of the class of biconservative surfaces with non-constant mean curvature in 4-dimensional space forms $N^4(\epsilon)$. Specifically, we focus on biconservative surfaces with non-parallel normalized…
In [2] we have classified the Blaschke quasi-umbilical submanifolds in the conformal space ${\mathbb Q}^n_s$. In this paper we shall classify the Blaschke para-umbilical hypersurfaces in the conformal space ${\mathbb Q}^n_s$. That may be…
We show that every indecomposable conical symplectic hypersurface of dimension four is isomorphic to the known one, namely, the Slodowy slice $X_n$ which is transversal to the nilpotent orbit of Jordan type $[2n-2, 1, 1]$ in the nilpotent…
The classification of 4-dimensional naturally reductive pseudo-Riemannian spaces is given. This classification comprises symmetric spaces, the product of 3-dimensional naturally reductive spaces with the real line and new families of…
The Hilbert space representations of a non-commutative q-deformed Minkowski space, its momenta and its Lorentz boosts are constructed. The spectrum of the diagonalizable space elements shows a lattice-like structure with accumulation points…
Using unfolded formulation of free equations for massless fields of all spins we obtain explicit form of higher-spin conformal conserved charges bilinear in 4d massless fields of arbitrary spins.
We investigate 3-dimensional complete minimal hypersurfaces in the hyperbolic space $\mathbb{H}^{4}$ with Gauss-Kronecker curvature identically zero. More precisely, we give a classification of complete minimal hypersurfaces with…
We classify totally geodesic and parallel hypersurfaces of four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds.
The extremal and partly marginally trapped surfaces in Minkowski 4-space, which are invariant under the group of boost isometries, are classified. Moreover, it is shown that there do not exist extremal surfaces of this kind with constant…
We prove three results in this paper. First, we prove for a wide class of functions $\varphi\in C^2(\mathbb{S}^{n-1})$ and $\psi(X, \nu)\in C^2(\mathbb{R}^{n+1}\times\mathbb{H}^n),$ there exists a unique, entire, strictly convex, spacelike…
Two special neutral hypersurfaces $\mathcal{L}_{\pm}$ in the light cone $L(\bigwedge^2 E^4_1 )$ studied in [1], [3] are $SO(3,1)$-orbits. In this paper, we see that each $SO(3,1)$-orbit in $L(\bigwedge^2 E^4_1 )$ is either a neutral…
We introduce the notion of Reeb parallel structure Jacobi operator for real hypersurfaces in the complex hyperbolic quadric ${Q^*}^m=SO^0_{2,m}/SO_2 SO_m$, $m \geq 3$, and give a classification theory for real hypersurfaces in ${{Q^*}^m}$,…
We study the class of spacelike surfaces in the four-dimensional Minkowski space whose mean curvature vector at any point is a non-zero spacelike vector or timelike vector. These surfaces are determined up to a motion by eight invariant…
This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…
In this study, we give weighted mean and weighted Gaussian curvatures of two types of timelike general rotational surfaces with non-null plane meridian curves in four-dimensional Minkowski space E^4_1 with density…
The class of surfaces in 3-space possessing nontrivial deformations which preserve principal directions and principal curvatures (or, equivalently, the shape operator) was investigated by Finikov and Gambier as far back as in 1933. We…
In this article we carry out a detailed investigation of the geometric nature of the points at infinity of Minkowski superspace. It turns out that there are several sets of points forming the superconformal boundary of Minkowski superspace:…
In this paper, we study hypersurfaces of Euclidean spaces with arbitrary dimension. First, we obtain some results on $\mbox{H}$-hypersurfaces. Then, we give the complete classification of $\mbox{H}$-hypersurfaces with 3 distinct curvatures.…