Open Access
December 2009 The Geometry of Generalised Cheeger-Gromoll Metrics
Michèle BENYOUNES, Eric LOUBEAU, Chris M. WOOD
Tokyo J. Math. 32(2): 287-312 (December 2009). DOI: 10.3836/tjm/1264170234

Abstract

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.

Citation

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Michèle BENYOUNES. Eric LOUBEAU. Chris M. WOOD. "The Geometry of Generalised Cheeger-Gromoll Metrics." Tokyo J. Math. 32 (2) 287 - 312, December 2009. https://doi.org/10.3836/tjm/1264170234

Information

Published: December 2009
First available in Project Euclid: 22 January 2010

zbMATH: 1200.53025
MathSciNet: MR2589947
Digital Object Identifier: 10.3836/tjm/1264170234

Subjects:
Primary: 53C07
Secondary: 53C20

Rights: Copyright © 2009 Publication Committee for the Tokyo Journal of Mathematics

Vol.32 • No. 2 • December 2009
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