DERIVATIONS ON CR MANIFOLDS

Title & Authors
DERIVATIONS ON CR MANIFOLDS
Ryu, Jeong-Seog; Yi, Seung-Hun;

Abstract
We studied the relation between the tangential Cauchy-Riemann operator $\small{{\={\partial}}_b}$ CR-manifolds and the derivation $\small{d^{{\pi}^{0,\;1}}}$ associated to the natural projection map $\small{{\pi}^{0.1}\;:\;TM\;{\bigotimes}\;{\mathbb{C}}\;=\;T^{1,0}\;{\bigoplus}\;T^{0,\;1}\;{\rightarrow}\;T^{0,\;1}}$. We found that these two differential operators agree only on the space of functions $\small{{\Omega}^0(M),\;unless\;T^{1,\;0}}$ is involutive as well. We showed that the difference is a derivation, which vanishes on $\small{{\Omega}^0(M)}$, and it is induced by the Nijenhuis tensor associated to $\small{{\pi}^{0.1}}$.
Keywords
derivation;tangential Cauchy-Riemann operator;CR-manifold;
Language
English
Cited by
References
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