On the CR analogue of Frankel conjecture and a smooth representative of the first Kohn-Rossi cohomology group

2019/05/21 by Chang, Der-Chen, Chang, Shu-Cheng, Kuo, Ting-Jung +1
#32V05 #32V20 (Primary) #53C56 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.08397

Abstract

In this note, we first give a criterion of pseudo-Einstein contact forms and then affirm the CR analogue of Frankel conjecture in a closed, spherical, strictly pseudoconvex CR manifold of nonnegative pseudohermitian curvature on the space of smooth representatives of the first Kohn-Rossi cohomology group. Moreover, we obtain the CR Frankel conjecture in a closed, spherical, strictly pseudoconvex CR manifold with the vanishing first Kohn-Rossi cohomology group. In particular, this conjecture holds in a spherical boundary of the Stein manifold.

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