## Tokyo Journal of Mathematics

### Quasi Contact Metric Manifolds with Constant Sectional Curvature

#### Abstract

A quasi contact metric manifold is a natural generalization of a contact metric manifold based on the geometry of the corresponding quasi Kahler cones. In this paper we prove that if a quasi contact metric manifold has constant sectional curvature $c$, then $c=1$; additionally, if the characteristic vector field is Killing, then the manifold is Sasakian. These facts are some generalizations of Olszak's theorem to quasi contact metric manifolds.

#### Article information

Source
Tokyo J. Math., Volume 41, Number 2 (2018), 515-525.

Dates
First available in Project Euclid: 26 January 2018

https://projecteuclid.org/euclid.tjm/1516935626

Mathematical Reviews number (MathSciNet)
MR3908807

Zentralblatt MATH identifier
07053489

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53D10: Contact manifolds, general

#### Citation

MALEK, Fereshteh; HOJATI, Rezvan. Quasi Contact Metric Manifolds with Constant Sectional Curvature. Tokyo J. Math. 41 (2018), no. 2, 515--525. https://projecteuclid.org/euclid.tjm/1516935626

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