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Volume 31 Number 2 2008 |
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Ricci Generalized Pseudo-Parallel Kaehlerian Submanifolds in Complex Space Forms
Ahmet Yildiz and Cengizhan Murathan
Abstract.
Let Mm(c) be a complex m-dimensional space form of holomorphic
sectional curvature c and M n be a complex n-dimensional Kaehlerian submanifold
of Mm(c). We prove that if M n is Ricci generalized pseudo-parallel, then
either M n is totally geodesic, or ||h||2 = -2 ⁄
3 (Lτ- 1 ⁄
2(n+2)c), or at some point
x of M n, ||h||2 (x) > -2 ⁄
3 (L(x)τ(x) - 1 ⁄
2(n+2)c).
2000 Mathematics Subject Classification: Primary 53B20, 53B25, 53B50; Secondary
53C15.
Full text: PDF
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