Minimal submanifolds with small total scalar curvature in Euclidean space

Minimal Lagrangian Submanifolds in Complex Euclidean Space

Slant submanifolds with prescribed scalar curvature into cosymplectic space form

In this paper, we have proved that locally there exist infinitely many three dimensional slant submanifolds with prescribed scalar curvature into cosymplectic space form M 5 (c) with c ∈ {−4, 4}while there does not exist flat minimal proper slant surface in M 5 (c) with c 6= 0. In section 5, we have established an inequality between mean curvature and sectional curvature of the subamnifold and ...

Cones in the Euclidean space with vanishing scalar curvature.

Given a hypersurface M on a unit sphere of the Euclidean space, we define the cone based on M as the set of half-lines issuing from the origin and passing through M. By assuming that the scalar curvature of the cone vanishes, we obtain conditions under which bounded domains of such cone are stable or unstable.

Construction of Hamiltonian-minimal Lagrangian Submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in the complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.

relating diameter and mean curvature for submanifolds of euclidean space

Given a closed m-dimensional manifold M immersed in R, we estimate its diameter d in terms of its mean curvature H by