A note on Chen's basic equality for submanifolds in a Sasakian space form

Mukut Mani Tripathi, Jeong-Sik Kim and Seon-Bu Kim

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-6

Abstract:

It is proved that a Riemannian manifold M isometrically immersed in a Sasakian space form M ˜ ( c ) of constant φ -sectional curvature c < 1 , with the structure vector field ξ tangent to M , satisfies Chen's basic equality if and only if it is a 3 -dimensional minimal invariant submanifold.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:217274

DOI: 10.1155/S0161171203201137

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