Geodesic
THE CALABI (VERONESE)IMBEDDINGS AS INTEGRAL SUBMANIFOLDS OF [Copf]P^{2n+1}
Glasgow mathematical journal, Tome 42 (2000) no. 2, pp. 183-193

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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. 
BLAIR, D. E.; KORKMAZ, B.; VRANCKEN, L. THE CALABI (VERONESE)IMBEDDINGS AS INTEGRAL SUBMANIFOLDS OF [Copf]P^{2n+1}. Glasgow mathematical journal, Tome 42 (2000) no. 2, pp. 183-193. doi: 10.1017/S0017089500020036
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     title = {THE {CALABI} {(VERONESE)IMBEDDINGS} {AS} {INTEGRAL} {SUBMANIFOLDS} {OF} {[Copf]P^{2n+1}}},
     journal = {Glasgow mathematical journal},
     pages = {183--193},
     year = {2000},
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     doi = {10.1017/S0017089500020036},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500020036/}
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