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THE CALABI (VERONESE)IMBEDDINGS AS INTEGRAL SUBMANIFOLDS OF [Copf]P^{2n+1}

Published online by Cambridge University Press:  01 May 2000

D. E. BLAIR ,
B. KORKMAZ  and
L. VRANCKEN
D. E. BLAIR
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan, U.S.A.
B. KORKMAZ
Affiliation:
Department of Mathematics, Middle East Technical University, Ankara, Turkey
L. VRANCKEN
Affiliation:
Fachbereich Mathematik, Technische Universität Berlin, D-10623 Berlin, Germany
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Abstract

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Considering odd-dimensional complex projective space as acomplex contact manifold, one may ask which of the Calabi (Veronese) imbeddings can be positioned by aholomorphic congruence as integral submanifolds of the complex contact structure. It is first shownthat when the first normal space is the whole normal space, this is impossible. It is also shown to beimpossibile for a Calabi surface (complex dimension 2) in complex projective space of dimension 9where one has both a first and second normal space. However when the complex dimension of thesubmanifold is odd and the whole normal space consists of the first and second normal spaces, thenthere is a holomorphic congruence positioning the Calabi imbedding as an integral submanifold of thecomplex contact structure.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 2 , May 2000 , pp. 183 - 193
Copyright
2000 Glasgow Mathematical Journal Trust