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Fernando Muro
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The unit tangent bundle of two2- or four manifolds4-manifolds as a principal $S^{1}$- or $S^{3}$ principle bundle-bundle

What type of obstructions have been studied for a Riemannian two (four) manifold for which so that the unit tangent bundle has an structureof a Riemannian 2-(4-)manifold have a structure of a principal $S^{1}$  -(  $S^{3}$  -)principle bundlebundle?

The unit tangent bundle of two or four manifolds as $S^{1}$ or $S^{3}$ principle bundle

What type of obstructions have been studied for a Riemannian two (four) manifold for which the unit tangent bundle has an structure of a $S^{1}$  (  $S^{3}$  )principle bundle?

The unit tangent bundle of 2- or 4-manifolds as a principal $S^{1}$- or $S^{3}$-bundle

What type of obstructions have been studied so that the unit tangent bundle of a Riemannian 2-(4-)manifold have a structure of a principal $S^{1}$-($S^{3}$-)bundle?

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Ali Taghavi
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The unit tangent bundle of two or four manifolds as $S^{1}$ or $S^{3}$ principle bundle

What type of obstructions have been studied for a Riemannian two (four) manifold for which the unit tangent bundle has an structure of a $S^{1}$ ( $S^{3}$ )principle bundle?