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December 2010 Compact Minimal $CR$ Submanifolds of a Complex Projective Space with Positive Ricci Curvature
Mayuko KON
Tokyo J. Math. 33(2): 415-434 (December 2010). DOI: 10.3836/tjm/1296483480

Abstract

We give a reduction theorem for the codimension of a compact $n$-dimensional minimal proper $CR$ submanifold $M$ immersed in a complex projective space $CP^m$ with complex structure $J$, under the assumption that the Ricci curvature of $M$ is equal to or greater than $n-1$. Moreover, we classify compact $n$-dimensional minimal $CR$ submanifolds whose Ricci tensor $S$ satisfies $S(X,X)\geq (n-1)g(X,X)+kg(PX,PX)$, $k=0,1,2$, for any vector field $X$ tangent to $M$, where $PX$ is the tangential part of $JX$.

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Mayuko KON. "Compact Minimal $CR$ Submanifolds of a Complex Projective Space with Positive Ricci Curvature." Tokyo J. Math. 33 (2) 415 - 434, December 2010. https://doi.org/10.3836/tjm/1296483480

Information

Published: December 2010
First available in Project Euclid: 31 January 2011

zbMATH: 1162.53316
MathSciNet: MR2779427
Digital Object Identifier: 10.3836/tjm/1296483480

Subjects:
Primary: 53C40
Secondary: 53C55

Rights: Copyright © 2010 Publication Committee for the Tokyo Journal of Mathematics

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Vol.33 • No. 2 • December 2010
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