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| ON A CONJECTURE OF K. OGIUE FOR KAEHLER HYPERSURFACES |
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Citation： |
Sheng Weiming.ON A CONJECTURE OF K. OGIUE FOR KAEHLER HYPERSURFACES[J].Chinese Annals of Mathematics B,1994,15(1):69~74 |
| Page view： 1002
Net amount： 639 |
Authors： |
Sheng Weiming; |
Foundation： |
Project supported by the National Natural ScienceFoundation of China |
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| Abstract： |
An affirmative answer to a conjecture of K. Ogiue formulated in
[2] is given, namely, the following result is proved:
Let $M^n\, (n\ge 2)$ be a complete Kaehler hypersurface immersed
in a complex projective space $CP^{n+1}$. If every sectional
curvature of $M^n$ is positive, then $M^n$ is totally geodesic in
$CP^{n+1}.$ |
Keywords： |
Kaehler hypersurfaces, Conjecture of K. Ogiue,Sectional curvature. |
Classification： |
58D10, 58D17 |
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