Tohoku Mathematical Journal

Submanifolds with constant scalar curvature in a unit sphere

Xi Guo and Haizhong Li

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

Article information

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

Dates
First available in Project Euclid: 12 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1378991019

Digital Object Identifier
doi:10.2748/tmj/1378991019

Mathematical Reviews number (MathSciNet)
MR3102538

Zentralblatt MATH identifier
1291.53073

Subjects
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]

Keywords
Scalar curvature mean curvature vector the second fundamental form

Citation

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. https://projecteuclid.org/euclid.tmj/1378991019


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