On the pseudohermitian sectional curvature of a strictly pseudoconvex CR manifold |
| |
Authors: | Elisabetta Barletta |
| |
Institution: | Università degli Studi della Basilicata, Dipartimento di Matematica, Contrada Macchia Romana, 85100 Potenza, Italy |
| |
Abstract: | 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 lengths 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 φ-sectional 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 ?2(n+1) and if dimRi(M,θ)=2(n+1) then Hθ(σ)= constant. |
| |
Keywords: | 32V05 53C25 53C30 32V40 |
本文献已被 ScienceDirect 等数据库收录! |
|