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.
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