Isotropic minimal submanifolds in a space form

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.

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.

RICCI CURVATURE OF SUBMANIFOLDS OF A SASAKIAN SPACE FORM

Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form...

Minimal Lagrangian Submanifolds in Complex Euclidean Space

Rigidity of Minimal Submanifolds in Space Forms

(1.1) Let c be a real number. Represent by A4"(c) a n-dimensional space form of curvature c. Let M N be a N-dimensional connected Riemannian manifold. The question that served as the starting point for this paper was to find simple conditions on the metric of M so that, if f:M"~ffl"+P(c), p>= 1, is an isometric minimal immersion then f is rigid in the following sense: given another minimal imme...