A pinching theorem on complete submanifolds with parallel mean curvature vectors

Ziqi Sun. "A pinching theorem on complete submanifolds with parallel mean curvature vectors." Colloquium Mathematicae 98.2 (2003): 189-199. <http://eudml.org/doc/285223>.

@article{ZiqiSun2003,
abstract = { 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 Okumura-Hasanis pinching theorem to the case of higher codimensions. },
author = {Ziqi Sun},
journal = {Colloquium Mathematicae},
language = {eng},
number = {2},
pages = {189-199},
title = {A pinching theorem on complete submanifolds with parallel mean curvature vectors},
url = {http://eudml.org/doc/285223},
volume = {98},
year = {2003},
}

TY - JOUR
AU - Ziqi Sun
TI - A pinching theorem on complete submanifolds with parallel mean curvature vectors
JO - Colloquium Mathematicae
PY - 2003
VL - 98
IS - 2
SP - 189
EP - 199
AB - 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 Okumura-Hasanis pinching theorem to the case of higher codimensions.
LA - eng
UR - http://eudml.org/doc/285223
ER -