Tohoku Mathematical Journal
2013
September
SECOND SERIES VOL. 65, NO. 3

Tohoku Math. J.
65 (2013), 331-339

Title SUBMANIFOLDS WITH CONSTANT SCALAR CURVATURE IN A UNIT SPHERE

Author Xi Guo and Haizhong Li

(Received June 27, 2012, revised November 30, 2012)
Abstract. We study the submanifolds in the unit sphere ${\boldsymbol S}^{n+p}$ with constant scalar curvature and parallel normalized mean curvature vector field. In this case, we can generalize the work of the second author about hypersurfaces in [8] to submanifolds in a unit sphere.

Mathematics Subject Classification. Primary 53C42; Secondary 53A10.
Key words and phrases. Scalar curvature, mean curvature vector, the second fundamental form.

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