Displaying similar documents to “Null 2-type space-like submanifolds of E t 5 with normalized parallel mean curvature vector.”

A pinching theorem on complete submanifolds with parallel mean curvature vectors

Ziqi Sun (2003)

Colloquium Mathematicae


Let M be an n-dimensional complete immersed submanifold with parallel mean curvature vectors in an (n+p)-dimensional Riemannian manifold N of constant curvature c > 0. Denote the square of length and the length of the trace of the second fundamental tensor of M by S and H, respectively. We prove that if S ≤ 1/(n-1) H² + 2c, n ≥ 4, or S ≤ 1/2 H² + min(2,(3p-3)/(2p-3))c, n = 3, then M is umbilical. This result generalizes the...

On the total (non absolute) curvature of a even dimensional submanifold X immersed in R.

A. M. Naveira (1994)

Revista Matemática de la Universidad Complutense de Madrid


The total curvatures of the submanifolds immersed in the Euclidean space have been studied mainly by Santaló and Chern-Kuiper. In this paper we give geometrical and topological interpretation of the total (non absolute) curvatures of the even dimensional submanifolds immersed in R. This gives a generalization of two results obtained by Santaló.

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 ) .