Warianty tytułu
Języki publikacji
Abstrakty
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.
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
189-199
Opis fizyczny
Daty
wydano
2003
Twórcy
autor
- Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67226, U.S.A.
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-2-5