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引用次数: 5
摘要
摘要对于接触流形，研究了Tanaka-Webster连接下具有常全纯截面曲率的强伪凸CR空间形式。我们证明了强伪凸CR空间形式M是弱局部伪埃米对称的当且仅当(i) dim M = 3， (ii) M是Sasakian空间形式，或(iii) M局部等距于恒定曲率- 1的双曲空间n+1的单位切线球束T1(n+1)。
Abstract For a contact manifold, we study a strongly pseudo-convex CR space form with constant holomorphic sectional curvature for the Tanaka-Webster connection. We prove that a strongly pseudo-convex CR space form M is weakly locally pseudo-Hermitian symmetric if and only if (i) dim M = 3, (ii) M is a Sasakian space form, or (iii) M is locally isometric to the unit tangent sphere bundle T1(n+1) of a hyperbolic space n+1 of constant curvature −1.
期刊介绍：
Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.
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