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On Ricci curvature of totally real submanifolds in a quaternion projective space

Ximin Liu (2002)

Archivum Mathematicum

Let M n be a Riemannian n -manifold. Denote by S ( p ) and Ric ¯ ( p ) the Ricci tensor and the maximum Ricci curvature on M n , respectively. In this paper we prove that every totally real submanifolds of a quaternion projective space Q P m ( c ) satisfies S ( ( n - 1 ) c + n 2 4 H 2 ) g , where H 2 and g are the square mean curvature function and metric tensor on M n , respectively. The equality holds identically if and only if either M n is totally geodesic submanifold or n = 2 and M n is totally umbilical submanifold. Also we show that if a Lagrangian submanifold of...

On riemannian foliations with minimal leaves

Jesús A. Alvarez Lopez (1990)

Annales de l'institut Fourier

For a Riemannian foliation, the topology of the corresponding spectral sequence is used to characterize the existence of a bundle-like metric such that the leaves are minimal submanifolds. When the codimension is 2 , a simple characterization of this geometrical property is proved.

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