Tsukuba Journal of Mathematics

Real hypersurfaces of a complex projective space satisfying a pointwise nullity condition

Abstract

In this paper, we give a classification of real hypersurfaces of a complex projective space $CP^{n}$ satisfying a pointwise nullity condition for the structure vector field $\xi$ i.e., $R(X, Y)\xi=k\{\eta(Y)X-\eta(X)Y\}$, $k$ is a function, and further we prove a local structure theorem of real hypersurfaces of $CP^{n}$ which satisfies $R(X, A\xi)\xi=k\{\eta(A\xi)X-\eta(X)A\xi\}$. The motivation of the present paper is a well-known fact that $CP^{n}$ does not admit a real hypersurface of constant curvature.

Article information

Source
Tsukuba J. Math., Volume 23, Number 2 (1999), 279-291.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496163873

Digital Object Identifier
doi:10.21099/tkbjm/1496163873

Mathematical Reviews number (MathSciNet)
MR1715479

Zentralblatt MATH identifier
0976.53018

Citation

Cho, Jong Taek; Ki, U-Hang. Real hypersurfaces of a complex projective space satisfying a pointwise nullity condition. Tsukuba J. Math. 23 (1999), no. 2, 279--291. doi:10.21099/tkbjm/1496163873. https://projecteuclid.org/euclid.tkbjm/1496163873