Contact Metric Spaces and pseudo-Hermitian Symmetry

Jong Taek Cho
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Jong Taek Cho: Department of Mathematics, Chonnam National University, Gwangju 61186, Korea

Mathematics, 2020, vol. 8, issue 9, 1-13

Abstract: We prove that a contact strongly pseudo-convex CR (Cauchy–Riemann) manifold M 2 n + 1 , n ≥ 2 , is locally pseudo-Hermitian symmetric and satisfies ∇ ξ h = μ h ? , μ ∈ R , if and only if M is either a Sasakian locally ? -symmetric space or a non-Sasakian ( k , μ ) -space. When n = 1 , we prove a classification theorem of contact strongly pseudo-convex CR manifolds with pseudo-Hermitian symmetry.

Keywords: contact almost CR (Cauchy–Riemann) manifold; generalized Tanaka-Webster connection; pseudo-Hermitian symmetric space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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