Geodesic
Pseudo-umbilical submanifolds of constant curvature Riemannian manifolds
Glasgow mathematical journal, Tome 43 (2001) no. 1, pp. 129-133

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Bai [1] gave an intrinsic integral inequality for compact minimal submanifolds of constant curvature Riemannian manifolds. In this paper, we extend Bai's result to the case of pseudo-umbilical submanifolds. 
Cao, Xi-Fang. Pseudo-umbilical submanifolds of constant curvature Riemannian manifolds. Glasgow mathematical journal, Tome 43 (2001) no. 1, pp. 129-133. doi: 10.1017/S0017089501010126
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