×

zbMATH — the first resource for mathematics

Some remarks on Riemannian manifolds with parallel Cotton tensor. (English) Zbl 1418.53041
Summary: 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.

MSC:
53C20 Global Riemannian geometry, including pinching
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
PDF BibTeX XML Cite
Full Text: DOI Euclid