## Kodai Mathematical Journal

### Curvature properties of homogeneous real hypersurfaces in nonflat complex space forms

#### Abstract

In this paper, we study curvature properties of all homogeneous real hypersurfaces in nonflat complex space forms, and determine their minimalities and the signs of their sectional curvatures completely. These properties reflect the sign of the constant holomorphic sectional curvature $c$ of the ambient space. Among others, for the case of $c$ < 0 there exist homogeneous real hypersurfaces with positive sectional curvature and also ones with negative sectional curvature, whereas for the case of $c$ > 0 there do not exist any homogeneous real hypersurfaces with nonpositive sectional curvature.

#### Article information

Source
Kodai Math. J., Volume 41, Number 2 (2018), 315-331.

Dates
First available in Project Euclid: 2 July 2018

https://projecteuclid.org/euclid.kmj/1530496844

Digital Object Identifier
doi:10.2996/kmj/1530496844

Mathematical Reviews number (MathSciNet)
MR3824853

Zentralblatt MATH identifier
06936455

#### Citation

Maeda, Sadahiro; Tamaru, Hiroshi; Tanabe, Hiromasa. Curvature properties of homogeneous real hypersurfaces in nonflat complex space forms. Kodai Math. J. 41 (2018), no. 2, 315--331. doi:10.2996/kmj/1530496844. https://projecteuclid.org/euclid.kmj/1530496844