Derivations on CR manifolds
Commun. Korean Math. Soc. 2004 Vol. 19, No. 1, 135-141
Printed March 1, 2004
Jeong Seog Ryu, Seunghun Yi
Hongik University, Youngdong University
Abstract : {\hskip-0.1cm}We studied the relation between the tangential Cauchy-Riemann operator $\overline \partial _b$ on CR-manifolds and the derivation $d^{\pi^{0,1}}$ associated to the natural projection map $\pi^{0,1}:TM \otimes {\mathbb C}=T^{1,0} \oplus T^{0,1} \to T^{0,1}$. We found that these two differential operators agree only on the space of functions $\Omega^0(M)$, unless $T^{1,0}$ is involutive as well. We showed that the difference is a derivation, which vanishes on $\Omega^0(M)$, and it is induced by the Nijenhuis tensor associated to $\pi^{0,1}$.
Keywords : derivation, tangential Cauchy-Riemann operator, CR-manifold
MSC numbers : 32W10, 13N15
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