Certain results on almost contact pseudo-metric manifolds

We study the geometry of almost contact pseudo-metric manifolds in terms of tensor fields h : = 1 2 £ ξ φ and ℓ : = R ( · , ξ ) ξ , emphasizing analogies and differences with respect to the contact metric case. Certain identities involving ξ -sectional curvatures are obtained. We establish necessary...

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Bibliographic Details
Published in:Journal of geometry 2019-08, Vol.110 (2), p.1-14, Article 41
Main Authors: Venkatesha, V., Naik, Devaraja Mallesha, Tripathi, Mukut Mani
Format: Article
Language:English
Subjects:
Geometry
Mathematics
Mathematics and Statistics
Tensors
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Summary:We study the geometry of almost contact pseudo-metric manifolds in terms of tensor fields h : = 1 2 £ ξ φ and ℓ : = R ( · , ξ ) ξ , emphasizing analogies and differences with respect to the contact metric case. Certain identities involving ξ -sectional curvatures are obtained. We establish necessary and sufficient condition for a nondegenerate almost CR structure ( H ( M ) , J , θ ) corresponding to almost contact pseudo-metric manifold M to be CR manifold. Finally, we prove that a contact pseudo-metric manifold ( M , φ , ξ , η , g ) is Sasakian pseudo-metric if and only if the corresponding nondegenerate almost CR structure ( H ( M ) , J ) is integrable and J is parallel along ξ with respect to the Bott partial connection.
ISSN:0047-2468
1420-8997
DOI:10.1007/s00022-019-0498-7