On the intrinsic normalizations of the seminonholonomic complexes \(SN Gr(m,n (m+1) (n-m)- \varrho)\). I. (English. Russian original) Zbl 0983.53008
Lith. Math. J. 39, No. 4, 408-425 (1999); translation from Liet. Mat. Rink. 39, No. 4, 517-538 (1999).
Summary: The first investigations of the differential geometry of the seminonholonomic ruled manifolds of the projective space were initiated by K. I. Grincevičius [Litov. Mat. Sb. 4, 329-334 (1964; Zbl 0189.21901)]. His ideas were further developed in the works of V. I. Bliznikas, S. I. Gregelionis, and others. The papers [G. F. Laptev and N. M. Ostianu, Trudy Geom. Semin., 3, 49-94 (1971)] and [N. M. Ostianu, ibid. 95-114 (1971)] are devoted to the study of the differential geometry of distributions of the \(m\)-dimensional linear elements in the space of projective connections. In the present note, we examine some questions concerning intrinsic normalizations of the seminonholonomic complexes \(SN Gr (m,n(m+1) (n-m)- \rho)\) of the projective space \(P_n\).
MSC:
| 53A20 | Projective differential geometry |
| 53C30 | Differential geometry of homogeneous manifolds |
| 53B10 | Projective connections |
| 53C05 | Connections (general theory) |
Keywords:
projective transformation; Grassmann manifold; distribution of \(m\)-planes; normalization of distribution; seminonholonomic complexes; projective spaceReferences:
| [1] | K. J. Grincevičius, On a complex of correlative elements,Liet. Matem. Rink.,4(3), 329–335 (1964). · Zbl 0189.21901 |
| [2] | G. F. Laptev and N. M. Ostianu, Distribution ofm-dimensional linear elements in a space of projective connection. I,Trudy Geom. Seminara, VINITI AN SSSR,3, 49–94 (1971). · Zbl 1396.53031 |
| [3] | H. M. Ostianu, Distribution ofm-dimensional linear elements in a space of projective connection. II,Trudy Geom. Seminara, VINITI AN SSSR,3, 95–114 (1971). · Zbl 1396.53032 |
| [4] | K. V. Navickis, Intrinsic normalizations of the seminonholonomic complexesSN Gr(m, n,(m+1)(n)), Lith. Math. J.,28(2), 162–174 (1988). · Zbl 0666.53005 · doi:10.1007/BF01027192 |
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