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- W2951620216 abstract "We consider manifolds endowed with metric contact pairs for which the two characteristic foliations are orthogonal. We give some properties of the curvature tensor and in particular a formula for the Ricci curvature in the direction of the sum of the two Reeb vector fields. This shows that metrics associated to normal contact pairs cannot be flat. Therefore flat non-Kahler Vaisman manifolds do not exist. Furthermore we give a local classification of metric contact pair manifolds whose curvature vanishes on the vertical subbundle. As a corollary we have that flat associated metrics can only exist if the leaves of the characteristic foliations are at most three-dimensional." @default.
- W2951620216 created "2019-06-27" @default.
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- W2951620216 date "2011-10-28" @default.
- W2951620216 modified "2023-09-26" @default.
- W2951620216 title "On the curvature of metric contact pairs" @default.
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- W2951620216 doi "https://doi.org/10.48550/arxiv.1110.6278" @default.
- W2951620216 hasPublicationYear "2011" @default.
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