Displaying similar documents to “Mean curvature comparison for tubular hypersurfaces in symmetric spaces.”

On an inequality of Oprea for Lagrangian submanifolds

Franki Dillen, Johan Fastenakels (2009)

Open Mathematics


We show that a Lagrangian submanifold of a complex space form attaining equality in the inequality obtained by Oprea in [8], must be totally geodesic.

A pointwise inequality in submanifold theory

P. J. De Smet, F. Dillen, Leopold C. A. Verstraelen, L. Vrancken (1999)

Archivum Mathematicum


We obtain a pointwise inequality valid for all submanifolds M n of all real space forms N n + 2 ( c ) with n 2 and with codimension two, relating its main scalar invariants, namely, its scalar curvature from the intrinsic geometry of M n , and its squared mean curvature and its scalar normal curvature from the extrinsic geometry of M n in N m ( c ) .