Tokyo Journal of Mathematics

On the Geometry of the Tangent Bundle with the Cheeger-Gromoll Metric

Sigmundur GUDMUNDSSON and Elias KAPPOS

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Abstract

Let $(M,g)$ be a Riemannian manifold of constant sectional curvature $\kappa$ and $(TM, \tilde{g})$ be the tangent bundle of $M$ equipped with the Cheeger-Gromoll metric induced by $g$. We give necessary and sufficient conditions for $TM$ having positive scalar curvature. This gives counterexamples to a stated theorem of Sekizawa.

Article information

Source
Tokyo J. of Math. Volume 25, Number 1 (2002), 75-83.

Dates
First available in Project Euclid: 5 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1244208938

Digital Object Identifier
doi:10.3836/tjm/1244208938

Mathematical Reviews number (MathSciNet)
MR1908215

Zentralblatt MATH identifier
1019.53017

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Citation

GUDMUNDSSON, Sigmundur; KAPPOS, Elias. On the Geometry of the Tangent Bundle with the Cheeger-Gromoll Metric. Tokyo J. of Math. 25 (2002), no. 1, 75--83. doi:10.3836/tjm/1244208938. https://projecteuclid.org/euclid.tjm/1244208938


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References

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