Geodesic
On some reducibility condition for principal bundles and its application to projective geometry of submanifolds
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 1003-1035

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In the present paper we prove some sufficient reducibility condition for principal bundles, which is adapted to study of submanifolds in homogeneous spaces. We apply the above condition to find the differential-geometrical criterion of Segre manifolds. 
@article{FPM_2001_7_4_a3,
     author = {V. V. Konnov},
     title = {On some reducibility condition for principal bundles and its application to projective geometry of submanifolds},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1003--1035},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a3/}
}
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V. V. Konnov. On some reducibility condition for principal bundles and its application to projective geometry of submanifolds. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 1003-1035. http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a3/