Affiliation:
1. Department of Mathematics, University of Haifa, Israel
Abstract
We introduce the weighted mixed curvature of an almost product (e.g.
foliated) Riemannian manifold equipped with a vector field. We define
several qth Ricci type curvatures, which interpolate between the weighed
sectional and Ricci curvatures. New concepts of the
?mixed-curvature-dimension condition? and ?synthetic dimension of a
distribution? allow us to renew the estimate of the diameter of a compact
Riemannian foliation and splitting results for almost product manifolds of
nonnegative/nonpositive weighted mixed scalar curvature. We also study the
Toponogov?s type conjecture on dimension of a totally geodesic foliation
with positive weighted mixed sectional curvature.
Publisher
National Library of Serbia
Cited by
3 articles.
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