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Journals and Conferences
In this article, we establish a sharp inequality involving δ-invariant introduced by Chen for submanifolds in quaternionic space forms of constant quaternionic sectional curvature with arbitrary codimension. Mathematics Subject Classification: 53B25, 53B35.
In this paper, we study some properties of ruled surfaces with non-degenerate second fundamental form in a 3-dimensional LorentzMinkowski space related to its the Gaussian curvature, the second Gaussian curvature and the mean curvature.
In this paper, we classify ruled surfaces in Lorentz-Minkowski 3-spaces satisfying some algebraic equations in terms of the second Gaussian curvature, the mean curvature and the Gaussian curvature.
The helicoidal surface is a generalization of rotation surface in a Minkowski space. We study helicoidal surfaces in a Minkowski 3-space in terms of their Gauss map and provide some examples of new classes of helicoidal surfaces with constant mean curvature in a Minkowski 3-space.
For the mean curvature vector field H and the Laplace operator ∆ of a submanifold in the Minkowski space, a submanifold satisfying the condition ∆H = f H + gC is known as a generalized null 2-type, where f and g are smooth functions, and C is a constant vector. The notion of generalized null 2-type submanifolds is a generalization of null 2-type… (More)
In the present paper, we study rotational surfaces in the three dimensional pseudo-Galilean space G3. Also, we characterize rotational surfaces in G3 in terms of the position vector field, Gauss map and Laplacian operator of the second fundamental form on the surface.
Our principal goal is to study the prescribed curvature problem in a manifold with density. In particular, we consider the Euclidean 3-space R3 with a positive density function eφ, where φ = −x2 − y2, (x, y, z) ∈ R3 and construct all the helicoidal surfaces in the space by solving the second-order non-linear ordinary differential equation with the weighted… (More)