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Advances in Geometry

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

Sergey Stepanov
  • Corresponding author
  • Department of Mathematics, Finance University, Leningradsky Prospect, 49-55, 125468, Moscow, Russia
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/ Irina Tsyganok
  • Department of Mathematics, Finance University, Leningradsky Prospect, 49-55, 125468, Moscow, Russia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-07-20 | DOI: https://doi.org/10.1515/advgeom-2017-0043


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.

Keywords: Complete Riemannian manifold; two complementary orthogonal distributions

MSC 2010: 53C20


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About the article

Received: 2017-02-03

Revised: 2017-03-20

Revised: 2017-04-11

Published Online: 2018-07-20

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

Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0043.

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