#### Vol. 306, No. 1, 2020

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Central splitting of manifolds with no conjugate points

### James Dibble

Vol. 306 (2020), No. 1, 95–114
##### Abstract

Each compact Riemannian manifold with no conjugate points admits a family of functions whose integrals vanish exactly when central Busemann functions split linearly. These functions vanish when all central Busemann functions are sub- or superharmonic. When central Busemann functions are convex or concave, they must be totally geodesic. These yield generalizations of the splitting theorems of O’Sullivan and Eberlein for manifolds with no focal points and, respectively, nonpositive curvature.

##### Keywords
no conjugate points, no focal points, Busemann function, center theorem
##### Mathematical Subject Classification 2010
Primary: 53C20, 53C24
Secondary: 53C22