PINCHING THEOREMS FOR TOTALLY REAL MINIMAL SUBMANIFOLDS IN CPn

Let M be an n-dimensional totally real minimal submanifold in CPn. 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 Tn ⊂ CPn. If M is semi-parallel and the scalar curvature τ, $n(n-1)\leq \tau \...

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Published inGlasgow mathematical journal Vol. 51; no. 2; pp. 331 - 339
Main Authors MURATHAN, CENGİZHAN, ÖZGÜR, CİHAN
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.05.2009
Subjects
53C20
53C40
53C42
Mathematics
53C42
53C20
53C40
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Summary:Let M be an n-dimensional totally real minimal submanifold in CPn. 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 Tn ⊂ CPn. 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 RPn.
Bibliography:istex:AAB216BB122DF04BAB841EC94DBC9CE00C7BF9F8
PII:S001708950900500X
ark:/67375/6GQ-273K3TMG-T
ArticleID:00500
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0017-0895
1469-509X
DOI:10.1017/S001708950900500X