## Kodai Mathematical Journal

### Some remarks on Riemannian manifolds with parallel Cotton tensor

#### Abstract

We give some sufficient conditions for stochastically complete Riemannian manifolds with parallel Cotton tensor to be either Einstein or of constant sectional curvature, and obtain an optimal pinching theorem. In particular, when $n$ = 4, we give a full classification.

#### Article information

Source
Kodai Math. J., Volume 42, Number 1 (2019), 64-74.

Dates
First available in Project Euclid: 19 March 2019

https://projecteuclid.org/euclid.kmj/1552982506

Digital Object Identifier
doi:10.2996/kmj/1552982506

Mathematical Reviews number (MathSciNet)
MR3934613

Zentralblatt MATH identifier
07081613

#### Citation

Fu, Hai-Ping; Xu, Gao-Bo; Tao, Yong-Qian. Some remarks on Riemannian manifolds with parallel Cotton tensor. Kodai Math. J. 42 (2019), no. 1, 64--74. doi:10.2996/kmj/1552982506. https://projecteuclid.org/euclid.kmj/1552982506