We show that a minimal disk satisfying the free boundary condition in a constant curvature ball of any dimension is totally geodesic. We weaken the condition to parallel mean curvature vector in which case we show that the disk lies in a three dimensional constant curvature submanifold and is totally umbilic. These results extend to higher dimensions earlier three dimensional work of J. C. C. N...

This research article attempts to investigate anti-invariant Lorentzian submersions and the Lagrangian (LLS) from concircular structure [in short (LCS) n ] manifolds onto semi-Riemannian with relevant non-trivial examples. It is shown that horizontal distributions of such are not integrable their fibers totally geodesic. As a result, they can be geodesic maps. Anti-invariant also explored for h...

We study relations between certain totally geodesic foliations of a closed flat manifold and its collapsed Gromov-Hausdorff limits. Our main results explicitly identify such limits as orbifolds, provide algebraic geometric criteria to determine whether they are singular.

In the last decades, several three‐dimensional face recognition algorithms have been thought, designed, and assessed. What they have in common can be hardly said, as they differ in theoretical background, tools, and method. Here we propose a new 3D face recognition algorithm, entirely developed in Matlab®, whose framework totally comes from Differential Geometry. Firstly, 17 soft‐tissue landmar...

We review the circumstances under which test particles can be localized around a spacetime section Σ0 smoothly contained within a codimension-1 embedding space M . If such a confinement is possible, Σ0 is said to be totally geodesic. Using three different methods, we derive a stability condition for trapped test particles in terms of intrinsic geometrical quantities on Σ0 and M ; namely, confin...

Let M be a compact (two-sided) minimal hypersurface in a Riemannian manifold M n+1 . It is a simple fact that if M has positive Ricci curvature then M cannot be stable (i. e. its Jacobi operator L has index at least one). If M = S(1) is the unit sphere and L has index one, then it is known that M must be a totally geodesic equator. We prove that if M is the real projective space RP = Sn+1(1)/{±...

Let F : Σ n × [0, T) → R n+m be a family of compact immersed submanifolds moving by their mean curvature vectors. We show the Gauss maps γ : (Σ n , g t) → G(n, m) form a harmonic heat flow with respect to the time-dependent induced metric g t. This provides a more systematic approach to investigating higher codimension mean curvature flows. A direct consequence is any convex function on G(n, m)...