On the pseudohermitian sectional curvature of a strictly pseudoconvex CR manifold
نویسنده
چکیده
We show that the pseudohermitian sectional curvature Hθ(σ) of a contact form θ on a strictly pseudoconvex CR manifold M measures the difference between the lengthes of a circle in a plane tangent at a point of M and its projection on M by the exponential map associated to the Tanaka-Webster connection of (M, θ). Any Sasakian manifold (M, θ) whose pseudohermitian sectional curvature Kθ(σ) is a point function is shown to be Tanaka-Webster flat, and hence a Sasakian space form of φsectional curvature c = −3. We show that the Lie algebra i(M, θ) of all infinitesimal pseudohermitian transformations on a strictly pseudoconvex CR manifold M of CR dimension n has dimension ≤ (n+ 1) and if dimR i(M, θ) = (n+ 1) then Hθ(σ) = constant.
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