Geodesic
Homogeneous and $\overline0$-homogeneous supermanifolds with retract $\mathbb{CP}^{1|4}_{kk20}$ when $k\ge 2$
Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 3, pp. 14-21 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper contain the description of non-split even-homogeneous supermanifolds over the complex projective line whose retract corresponds to a holomorphic vector bundle of the signature $(k,k,2,0),$ where $k\ge 2$. We prove that there are no non-split homogeneous supermanifolds in this case. See [3] and [4] for more information about the complex supermanifolds theory.
Keywords: complex supermanifold, homogeneous complex supermanifold, tangent sheaf.
Mots-clés : retract 
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M. A. Bashkin. Homogeneous and $\overline0$-homogeneous supermanifolds with retract $\mathbb{CP}^{1|4}_{kk20}$ when $k\ge 2$. Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 3, pp. 14-21. http://geodesic.mathdoc.fr/item/MAIS_2009_16_3_a1/

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[2] V. A. Bunegina, A. L. Onischik, “Odnorodnye supermnogoobraziya, svyazannye s kompleksnoi proektivnoi pryamoi”, Sovremennaya matematika i ee prilozheniya, 19, VINITI, Moskva, 2001, 141–180 | MR | Zbl

[3] A. L. Onischik, “Problemy klassifikatsii kompleksnykh supermnogoobrazii”, Matematika v Yaroslavskom universitete, Sb. obzornykh statei. K 25-letiyu matematicheskogo fakulteta, YarGU, Yaroslavl, 2001, 7–34 | MR

[4] V. A. Bunegina, A. L. Onishchik, “Two families of flag supermanifolds”, Different. Geom. and its Appl., 4 (1994), 329–360 | DOI | MR | Zbl

[5] A. L. Onishchik, “A Construction of Non-Split Supermanifolds”, Annals of Global Analysis and Geometry, 16 (1998), 309–333 | DOI | MR | Zbl