The tangent bundle of a ruled surface

Ganong, Richard; Russell, Peter B.

doi:10.1007/bf01456133

Cited by 5 publications

(1 citation statement)

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“…The total space M l 1 ,l 2 ,ρ of the principal S 1 bundle over Σ g × ρ CP 1 whose Euler class is l 1 [ω 1 ] + l 2 [ω 2 ] has a natural Sasakian structure S l 1 ,l 2 with constant scalar curvature. Now by [GR85] the holomorphic tangent bundle to Σ g × ρ CP 1 splits as a sum of holomorphic line bundles. This implies that the contact bundle D on M l 1 ,l 2 ,ρ splits as D = D 1 ⊕ D 2 .…”

Section: Proposition 33 Impliesmentioning

confidence: 99%

Reducibility in Sasakian geometry

Boyer¹,

Huang²,

Legendre

et al. 2018

Trans. Amer. Math. Soc.

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The purpose of this paper is to study reducibility properties in Sasakian geometry. First we give the Sasaki version of the de Rham Decomposition Theorem; however, we need a mild technical assumption on the Sasaki automorphism group which includes the toric case. Next we introduce the concept of cone reducible and consider S 3 bundles over a smooth projective algebraic variety where we give a classification result concerning contact structures admitting the action of a 2-torus of Reeb type. In particular, we can classify all such Sasakian structures up to contact isotopy on S 3 bundles over a Riemann surface of genus greater than zero. Finally, we show that in the toric case an extremal Sasaki metric on a Sasaki join always splits.

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Section: Proposition 33 Impliesmentioning

confidence: 99%