A trans-Sasakian 3-manifold is pseudo-symmetric if and only if it is η-Einstein. In particular, a quasi-Sasakian 3-manifold is pseudo-symmetric if and only if it is a coKähler manifold or a homothetic Sasakian manifold. Some examples of non-Sasakian pseudo-symmetric contact 3-manifolds are exhibited.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-1-7,
author = {Jong Taek Cho and Jun-ichi Inoguchi and Ji-Eun Lee},
title = {Pseudo-symmetric contact 3-manifolds III},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {77-98},
zbl = {1163.53017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-1-7}
}
Jong Taek Cho; Jun-ichi Inoguchi; Ji-Eun Lee. Pseudo-symmetric contact 3-manifolds III. Colloquium Mathematicae, Tome 116 (2009) pp. 77-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-1-7/