Tokyo Journal of Mathematics
- Tokyo J. Math.
- Volume 32, Number 2 (2009), 287-312.
The Geometry of Generalised Cheeger-Gromoll Metrics
We study the geometry of the tangent bundle equipped with a two-parameter family of metrics, deforming the Sasaki and Cheeger-Gromoll metrics. After deriving the expression for the Levi-Civita connection, we compute the Riemann curvature tensor and the sectional, Ricci and scalar curvatures. We identify all metrics whose restrictions to the fibres have positive sectional curvature. When the base manifold is a space form, we characterise metrics with non-negative sectional curvature and show that one can always find parameters ensuring positive scalar curvature. This extends to compact manifolds and, under some curvature conditions, to general manifolds.
Tokyo J. Math., Volume 32, Number 2 (2009), 287-312.
First available in Project Euclid: 22 January 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C07: Special connections and metrics on vector bundles (Hermite-Einstein- Yang-Mills) [See also 32Q20]
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
BENYOUNES, Michèle; LOUBEAU, Eric; WOOD, Chris M. The Geometry of Generalised Cheeger-Gromoll Metrics. Tokyo J. Math. 32 (2009), no. 2, 287--312. doi:10.3836/tjm/1264170234. https://projecteuclid.org/euclid.tjm/1264170234