PINCHING THEOREMS FOR TOTALLY REAL MINIMAL SUBMANIFOLDS IN CPn

被引：0

作者：

Murathan, Cengizhan ^{[1
]}

Ozgur, Cihan ^{[2
]}

机构：

[1] Uludag Univ, Dept Math, TR-16059 Bursa, Turkey

[2] Balikesir Univ, Dept Math, TR-10145 Balikesir, Turkey

来源：

GLASGOW MATHEMATICAL JOURNAL | 2009年 / 51卷

关键词：

SPACE; FORM;

D O I：

10.1017/S001708950900500X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be an n-dimensional totally real minimal submanifold in CPn. We prove that if M is semi-parallel and the scalar curvature tau, -(n-1)(n-2)(n+1)/2 <= tau <= 0, then M is an open part of the Clifford torus T-n subset of CPn. If M is semi-parallel and the scalar curvature tau, n(n - 1) <= tau <= n(3)-3n+2/2, then M is an open part of the real projective space RPn.

引用

页码：331 / 339

页数：9

共 15 条

[1] Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces
Amarzaya, A
Ohnita, Y
[J]. TOHOKU MATHEMATICAL JOURNAL, 2003, 55 (04) : 583 - 610
[2] [Anonymous], 1976, Lecture Notes in Pure and Applied Mathematics
[3] Calabi E., 1958, MICH MATH J, V5, P105, DOI 10.1307/mmj/1028998055
[4] TOTALLY REAL SUBMANIFOLDS
CHEN, BY
OGIUE, K
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 193 (JUN) : 257 - 266
[5] Deprez J, 1986, REND SEM U POLITEC T, V44, P303
[6] Deprez J., 1985, J. Geom., V25, P192
[7] SEMI-PARALLEL HYPERSURFACES OF A REAL SPACE FORM
DILLEN, F
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1991, 75 (2-3) : 193 - 202
[8] TOTALLY-REAL MINIMAL SUB-MANIFOLDS IN A COMPLEX PROJECTIVE-SPACE
EJIRI, N
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 86 (03) : 496 - 497
[9] IMMERSIONS WITH PARALLEL SECOND FUNDAMENTAL FORM
FERUS, D
[J]. MATHEMATISCHE ZEITSCHRIFT, 1974, 140 (01) : 87 - 92
[10] TOTALLY-REAL MINIMAL SUBMANIFOLDS IN CP(N)
LI, AM
ZHAO, GS
[J]. ARCHIV DER MATHEMATIK, 1994, 62 (06) : 562 - 568

← 1 2 →