On Ricci curvature of totally real submanifolds in a quaternion projective space
Liu, Ximin
Archivum Mathematicum, Tome 038 (2002), p. 297-305 / Harvested from Czech Digital Mathematics Library
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Let $M^n$ be a Riemannian $n$-manifold. Denote by $S(p)$ and $\overline{\operatorname{Ric}}(p)$ 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 $QP^m(c)$ satisfies $S\le ((n-1)c+\frac{n^2}{4}H^2)g$, 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 $QP^m(c)$ satisfies $\overline{\operatorname{Ric}}=(n-1)c+\frac{n^2}{4}H^2$ identically, then it is minimal.

Publié le : 2002-01-01
Classification:  53C26,  53C40,  53C42 
@article{107843,
     author = {Ximin Liu},
     title = {On Ricci curvature of totally real submanifolds in a quaternion projective space},
     journal = {Archivum Mathematicum},
     volume = {038},
     year = {2002},
     pages = {297-305},
     zbl = {1090.53052},
     mrnumber = {1942659},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107843}
}

Liu, Ximin. On Ricci curvature of totally real submanifolds in a quaternion projective space. Archivum Mathematicum, Tome 038 (2002) pp. 297-305. http://gdmltest.u-ga.fr/item/107843/

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