Positivity in Foliated Manifolds and Geometric Applications
Yashan Zhang, Tao Zheng
TL;DR
This paper introduces a new notion of positivity for certain cohomology classes on foliated manifolds, exploring its geometric implications and connections to curvature properties.
Contribution
It defines positivity for real basic (1,1) classes in basic Bott-Chern cohomology on foliated manifolds and investigates its geometric consequences.
Findings
Positivity relates to negativity of transverse holomorphic sectional curvature.
Provides new insights into geometric structures on foliated manifolds.
Establishes links between cohomology positivity and curvature properties.
Abstract
We introduce the notion of positivity for a real basic class in basic Bott-Chern cohomology group on foliated manifolds, and study the relationship between this positivity and the negativity of transverse holomorphic sectional curvature and give some geometric applications.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology