We prove some pinching theorems with respect to the scalar curvature of 4-dimensional conformally flat (concircularly flat, quasi-conformally flat) totally real minimal submanifolds in QP⁴(c).
Let be a Riemannian -manifold. Denote by and the Ricci tensor and the maximum Ricci curvature on , respectively. In this paper we prove that every totally real submanifolds of a quaternion projective space satisfies , where and are the square mean curvature function and metric tensor on , respectively. The equality holds identically if and only if either is totally geodesic submanifold or and is totally umbilical submanifold. Also we show that if a Lagrangian submanifold of...
We consider an almost Kenmotsu manifold with the characteristic vector field ξ belonging to the (k,μ)’-nullity distribution and h’ ≠ 0 and we prove that is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a flat n-dimensional manifold, provided that is ξ-Riemannian-semisymmetric. Moreover, if is a ξ-Riemannian-semisymmetric almost Kenmotsu manifold such that ξ belongs to the (k,μ)-nullity distribution, we prove that is...
We give the definition of -biminimal submanifolds and derive the equation for -biminimal submanifolds. As an application, we give some examples of -biminimal manifolds. Finally, we consider -minimal hypersurfaces in the product space and derive two rigidity theorems.
In this paper, by using Cheng-Yau’s self-adjoint operator , we study the complete hypersurfaces in a sphere with constant scalar curvature.
A new class of -dimensional Lorentz spaces of index is introduced which satisfies some geometric conditions and can be regarded as a generalization of Lorentz space form. Then, the compact space-like hypersurface with constant scalar curvature of this spaces is investigated and a gap theorem for the hypersurface is obtained.
In this paper, we study the stability of space-like hypersurfaces with constant scalar curvature immersed in the de Sitter spaces.
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