Geodesic
Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions
Glasgow mathematical journal, Tome 41 (1999) no. 1, pp. 33-41

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First we define the notion of k-Ricci curvature of a Riemannian n-manifold. Then we establish sharp relations between the k-Ricci curvature and the shape operator and also between the k-Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Several applications of such relationships are also presented. 
CHEN, BANG-YEN. Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions. Glasgow mathematical journal, Tome 41 (1999) no. 1, pp. 33-41. doi: 10.1017/S0017089599970271
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