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A remark on the mixed scalar curvature of a manifold with two orthogonal totally umbilical distributions

  • Sergey Stepanov EMAIL logo and Irina Tsyganok
Published/Copyright: July 20, 2018
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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.

MSC 2010: 53C20

Acknowledgement

We thank our referee for extensive comments and helpful remarks.

  1. Communicated by: P. Eberlein

  2. Funding: Our work was supported by RBRF grant 16-01-00053-a (Russia).

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Received: 2017-02-03
Revised: 2017-03-20
Revised: 2017-04-11
Published Online: 2018-07-20
Published in Print: 2019-07-26

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