We establish the Brunn-MINKOWSKI-type inequality for Lp-dual mixed volumes of star duality of mixed intersection bodies.

In this paper, the time-like hyperruled surfaces in the MINKOWSKI 4-space and their algebraic invariants are worked. Also some characteristic results are found about these algebraic invariants.

In this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. It gives some criterions to study locally convex topological spaces in a discrete approach.

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Isoparametric hypersurfaces of Lorentz-MINKOWSKI spaces, which has been classi, ed by M. A. Magid in 1985, have motivated some researchers to study biconservative hypersurfaces. A biconservative hy-persurface has conservative stress-energy with respect to the bienergy FUNCTIONAL...

In this paper, two new Hamilton operators are defined and the algebra of dual split quaternions is developed using these operators. It is shown that finite screw motions in MINKOWSKI 3-space can be expressed by dual-number r (3×3) matrices in dual Lorentzian space. Moreover, by means of Hamilton operators, screw motion is obtained in 3-dimensional MINKOWSKI space R31.

On a real vector space V, a Randers norm ^ F is de, ned by ^ F = ^, + ^ , , where ^,is a Euclidean norm and ^ ,is a covector. We show that the unit sphere ,in the Randers space (V,^ F) has positive ag curvature, if and only if j ^ , j^,< (5 􀀀,p 17)=2 ,0: 43845, thus answering a problem proposed by Prof. Zhongmin Shen. Moreover, we prove that the ag curvature of ,has a universal lower bound 􀀀, 4.

In this paper we study translation surfaces with the nondegenerate third fundamental form in Lorentz-MINKOWSKI space L3. As a result, we classify translation surfaces satisfying an equation in terms of the position vector  eld and the Laplace operator with respect to the third fundamental form III on the surface.

A hypersurface $ M^n $ in the Lorentz-MINKOWSKI space $\mathbb{L}^{n+1} $ is called $ L_k $-biharmonic if the position vector $ \psi $ satisfies the condition $ L_k^2\psi =0$, where $ L_k$ is the linearized operator of the $(k+1)$-th mean curvature of $ M $ for a fixed $k=0,1,\ldots,n-1$. This definition is a natural generalization of the concept of a biharmonic hypersurface. We prove that any $ L_k $-biharmonic surface in $ \mathbb{L}^3 $ is $k$-maximal. We also prove that any $ L_k $-biharmonic hypersurface in $ \mathbb{L}^4 $ with constant $ k$-th mean curvature is $ k $-maximal. These results give a partial answer to the Chen's conjecture for $L_k$-operator that $L_k$-biharmonicity implies $L_k$-maximality.