Tohoku Mathematical Journal

Submanifolds with constant scalar curvature in a unit sphere

Xi Guo and Haizhong Li

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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 Hypersurfaces with constant scalar curvature in space forms to submanifolds in a unit sphere.

Article information

Tohoku Math. J. (2), Volume 65, Number 3 (2013), 331-339.

First available in Project Euclid: 12 September 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

Scalar curvature mean curvature vector the second fundamental form


Guo, Xi; Li, Haizhong. Submanifolds with constant scalar curvature in a unit sphere. Tohoku Math. J. (2) 65 (2013), no. 3, 331--339. doi:10.2748/tmj/1378991019.

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