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Levi–Tanaka algebras and homogeneous $C R$ manifolds

Published online by Cambridge University Press:  04 December 2007

C. MEDORI  and
M. MACINOVICH
C. MEDORI
Affiliation:
S.I.S.S.A., Trieste, Italy
M. MACINOVICH
Affiliation:
Dipartimento di Matematica, Università di Pisa, via F. Buonarroti 2, 56127 Pisa, Italy; e-mail: [email protected]
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Abstract

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In this paper we take up the problem of discussing $C R$ manifolds of arbitrary $C R$ codimension. We closely follow the general method of N. Tanaka, while concentrating our attention to the case of manifolds endowed with partial complex structures. This study required a deeper understanding of the structure of the Levi–Tanaka algebras, which are the canonical prolongation of pseudocomplex fundamental graded Lie algebras. These algebras enjoy special properties, the understanding of which provided also a way to build up several different examples and points to a rich field of investigations. Here we restrained further our consideration to the homogeneous models.

Keywords

$C R$ manifoldLevi–Tanaka algebra
Type
Research Article
Information
Compositio Mathematica , Volume 109 , Issue 2 , August 1997 , pp. 195 - 250
Copyright
© 1997 Kluwer Academic Publishers