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Sasakian Metrics with an Additional Contact Structure

Volume 14, Number 2 (2012), 118 - 133

Sasakian Metrics with an Additional Contact Structure

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Abstract

The question of whether a Sasakian metric can admit an additional compatible (K)-contact structure is addressed. In the complete case if the second structure is also assumed Sasakian, works of Tachibana-Yu and Tanno show that the manifold must be 3-Sasakian or an odd dimensional sphere with constant curvature. Some extensions of this result are obtained, mainly in dimensions 3 and 5.