# A New Approach to the Local Embedding Theorem of CR-structures of N 4 (the Local Solvability for the Operator B in the Abstract Sense)

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This book is aimed at researchers in complex analysis, several complex variables, or partial differential equations. Kuranishi proved that any abstract strongly pseudo convex CR-structure of real dimension \$\geq 9\$ can be locally embedded in a complex euclidean space. For the case of real dimension \$=3\$, there is the famous Nirenberg counter example, but the cases of real dimension \$=5\$ or 7 were left open. The author of this book establishes the result for real dimension \$=7\$ and, at the same time, presents a new approach to Kuranishi's result.