## Journal of the Mathematical Society of Japan

### Curvature pinching for totally real submanifolds of a complex projective space

Yoshio MATSUYAMA

#### Abstract

Montiej Ros and Urbano [M3] showed a complete characterization of compact totally real minimal submanifold $M$ of $CP^{n}(c)$ with Ricci curvature $S$ of $M$ satisfying $S\geq 3(n-2)c/16$. The purpose of this paper is to answer Ogiue's conjecture which the above result remains true under the weaker condition of the scalar curvature $p$ of $M$ satisfying $p\geq 3n(n-2)c/16$.

#### Article information

Source
J. Math. Soc. Japan, Volume 52, Number 1 (2000), 51-64.

Dates
First available in Project Euclid: 10 June 2008

https://projecteuclid.org/euclid.jmsj/1213107655

Digital Object Identifier
doi:10.2969/jmsj/05210051

Mathematical Reviews number (MathSciNet)
MR1727200

Zentralblatt MATH identifier
0961.53033

Subjects