A pinching theorem on complete submanifolds with parallel mean curvature vectors

• Autorzy: Ziqi Sun
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53C40: Global submanifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 98
• Numer: 2
• Strony: 189-199

Daty

wydano

2003

Twórcy

autor

Ziqi Sun

• Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67226, U.S.A.

Identyfikatory

DOI

10.4064/cm98-2-5