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On rank one symmetric space

Inkang Kim (2004/2005)

Séminaire de théorie spectrale et géométrie

In this paper we survey some recent results on rank one symmetric space.

On real Kähler Euclidean submanifolds with non-negative Ricci curvature

Luis A. Florit, Wing San Hui, F. Zheng (2005)

Journal of the European Mathematical Society

We show that any real Kähler Euclidean submanifold f : M 2 n 2 n + p with either non-negative Ricci curvature or non-negative holomorphic sectional curvature has index of relative nullity greater than or equal to 2 n 2 p . Moreover, if equality holds everywhere, then the submanifold must be a product of Euclidean hypersurfaces almost everywhere, and the splitting is global provided that M 2 n is complete. In particular, we conclude that the only real Kähler submanifolds M 2 n in 3 n that have either positive Ricci curvature or...

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...

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