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.
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.
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 helicoidal surfaces in the three-dimensional isotropic space I 3 and construct helicoidal surfaces satisfying a linear equation in terms of the Gaussian curvature and the mean curvature of the surface.
In this paper, we establish an improved Chen inequality between the pseudo-Ricci curvature and the square of pseudo mean curvature with respect to the Tanaka-Webster connection in Sasakian space forms, and also we study an improved Chen inequality for anti-invariant submanifolds. The equality case is considered.
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.
We establish inequalities between the Ricci curvature and the squared mean curvature, and also between the k-Ricci curvature and the scalar curvature for a slant, semi-slant, and bi-slant submanifold in a locally conformal almost cosymplectic manifold with arbitrary codimension. Let M be a (2m + 1)-dimensional almost contact manifold with almost contact… (More)