Abstract
We prove a Liouville-type theorem for two orthogonal complementary totally umbilical distributions on a complete Riemannian manifold with non-positive mixed scalar curvature. This is applied to some special types of complete doubly twisted and warped products of Riemannian manifolds.
Acknowledgement
We thank our referee for extensive comments and helpful remarks.
Communicated by: P. Eberlein
Funding: Our work was supported by RBRF grant 16-01-00053-a (Russia).
References
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Articles in the same Issue
- Frontmatter
- A remark on the mixed scalar curvature of a manifold with two orthogonal totally umbilical distributions
- On mixed Lp John ellipsoids
- Valuations on convex functions and convex sets and Monge–Ampère operators
- Weierstrass points on Kummer extensions
- The Bonnet problem for harmonic maps to the three-sphere
- Maximal arcs in projective planes of order 16 and related designs
- On the decomposition of the small diagonal of a K3 surface
- Doubly transitive dimensional dual hyperovals: universal covers and non-bilinear examples
- Higgs bundles and fundamental group schemes
- A relation between the curvature ellipse and the curvature parabola
- Non-orientable three-submanifolds of G2-manifolds
- The growth of the first non-Euclidean filling volume function of the quaternionic Heisenberg group
- A class of analytic pairs of conjugate functions in dimension three
Articles in the same Issue
- Frontmatter
- A remark on the mixed scalar curvature of a manifold with two orthogonal totally umbilical distributions
- On mixed Lp John ellipsoids
- Valuations on convex functions and convex sets and Monge–Ampère operators
- Weierstrass points on Kummer extensions
- The Bonnet problem for harmonic maps to the three-sphere
- Maximal arcs in projective planes of order 16 and related designs
- On the decomposition of the small diagonal of a K3 surface
- Doubly transitive dimensional dual hyperovals: universal covers and non-bilinear examples
- Higgs bundles and fundamental group schemes
- A relation between the curvature ellipse and the curvature parabola
- Non-orientable three-submanifolds of G2-manifolds
- The growth of the first non-Euclidean filling volume function of the quaternionic Heisenberg group
- A class of analytic pairs of conjugate functions in dimension three