nLab Cheeger-Gromoll splitting theorem

This page is about the statement in Riemannian geometry. For the splitting principle (in algebraic topology) see there.

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Idea

On the classification of Riemannian manifolds with non-negative Ricci curvature

References

• Jeff Cheeger, Detlef Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geom. Volume 6, Number 1 (1971), 119-128 (euclid:1214430220)

• Arthur E. Fischer, Joseph A. Wolf, The structure of compact Ricci-flat Riemannian manifolds J. Differential Geom. 10 (1975), no. 2, 277–288 (euclid:jdg/1214432794)

See also

• Wikipedia, Splitting theorem

• Bobby Acharya, Section 1.2 of Supersymmetry, Ricci Flat Manifolds and the String Landscape (arXiv:1906.06886)