PINCHING THEOREMS FOR TOTALLY REAL MINIMAL SUBMANIFOLDS IN CP n
Abstract Let M be an n -dimensional totally real minimal submanifold in CP n . We prove that if M is semi-parallel and the scalar curvature τ, $\frac{-(n-1)(n-2)(n+1)}{2}\leq \tau \leq 0$ , then M is an open part of the Clifford torus T n ⊂ CP n . If M is semi-parallel and the scalar curvature τ, $n...
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| Published in | Glasgow mathematical journal Vol. 51; no. 2; pp. 331 - 339 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
01.05.2009
|
| Online Access | Get full text |
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| Summary: | Abstract
Let
M
be an
n
-dimensional totally real minimal submanifold in
CP
n
. We prove that if
M
is semi-parallel and the scalar curvature τ,
$\frac{-(n-1)(n-2)(n+1)}{2}\leq \tau \leq 0$
, then
M
is an open part of the Clifford torus
T
n
⊂
CP
n
. If
M
is semi-parallel and the scalar curvature τ,
$n(n-1)\leq \tau \leq \frac{n^{3}-3n+2}{2}$
, then
M
is an open part of the real projective space
RP
n
. |
|---|---|
| ISSN: | 0017-0895 1469-509X |
| DOI: | 10.1017/S001708950900500X |