When does a simply connected Lie group with an invariant metric of positive sectional curvature is compact?

The point of the question is: does this hypothesis provide to the positive sectional curvature metric a positive inferior bound for Ricci curvature in the sense of Bonnet-Meyers's theorem? If not, in which conditions is it possible? Is there any counterexample? If Bonnet-Meyers is not satisfected, is yet the group compact? I mean, does there any obstruction in therms of the Lie algebra of the group?

Thanks

When is a simply connected Lie group with an invariant metric of positive sectional curvature compact?

The point of the question is: does this hypothesis provide a positive lower bound on Ricci curvature in the sense of Bonnet-Meyers's theorem on the metric of positive sectional curvature? If not, under what conditions is it possible? Is there any counterexample? If Bonnet-Meyers is not satisfied, is the group still compact? I mean, are there any obstructions in terms of the Lie algebra of the group?

Thanks

When does a simply connected Lie group with an invariant metric of positive sectional curvature is compact?

The point of the question is: does this hypothesis provide to the positive sectional curvature metric an positive inferior bound for Ricci curvature in the sense of Bonnet-Meyers's theorem? If not, in which conditions is it possible? Is there any counterexample? If Bonnet-Meyers is not satisfected, is yet the group compact? I mean, does there any obstruction in therms of the Lie algebra of the group?

Thanks

When does a simply connected Lie group with an invariant metric of positive sectional curvature is compact?

The point of the question is: does this hypothesis provide to the positive sectional curvature metric a positive inferior bound for Ricci curvature in the sense of Bonnet-Meyers's theorem? If not, in which conditions is it possible? Is there any counterexample? If Bonnet-Meyers is not satisfected, is yet the group compact? I mean, does there any obstruction in therms of the Lie algebra of the group?

Thanks