Existence and uniqueness theorems for pointwise slant immersions in complex space forms

Ideal Slant Submanifolds in Complex Space Forms

Roughly speaking, an ideal immersion of a Riemannian manifold into a space form is an isometric immersion which produces the least possible amount of tension from the ambient space at each point of the submanifold. Recently, B.-Y. Chen studied Lagrangian submanifolds in complex space forms which are ideal. He proved that such submanifolds are minimal. He also classified ideal Lagrangian submani...

Uniqueness Theorems for Free Boundary Minimal Disks in Space Forms

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...

Minimal Lagrangian isotropic immersions in indefinite complex space forms

Shape Operator of Slant Submanifolds in Kenmotsu Space Forms

Isotropic Lagrangian Submanifolds in Complex Space Forms

In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in . We also give a classification of semi-parallel Lagrangian H-umbilical submanifolds.