Geodesic
Grassmann manifold $V\sp 4\sb 3$ in the projective space $P\sb 7$ with characteristics consisting of a quadric and two planes
Mathematica Bohemica, Tome 118 (1993) no. 3, pp. 225-240

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
Some results in the geometry of four-parametric manifolds of three-dimensional spaces in the projective space $P_7$ are found. The properties of such a manifold $V^4_3$ with characteristics consisting of a quadric and two planes are studied. The properties of the manifold dual to $V^4_3$ are found. Some results in the geometry of linear spaces from [1],[2],[3],[4] are used. The notation of the quantities is the same as in [4].
Some results in the geometry of four-parametric manifolds of three-dimensional spaces in the projective space $P_7$ are found. The properties of such a manifold $V^4_3$ with characteristics consisting of a quadric and two planes are studied. The properties of the manifold dual to $V^4_3$ are found. Some results in the geometry of linear spaces from [1],[2],[3],[4] are used. The notation of the quantities is the same as in [4].
DOI : 10.21136/MB.1993.125928
Classification : 53A20
Keywords: systems of linear spaces; dual manifold; four-parametric manifolds; projective space; characteristics; differential geometry of systems of linear spaces 
Vala, Josef. Grassmann manifold $V\sp 4\sb 3$ in the projective space $P\sb 7$ with characteristics consisting of a quadric and two planes. Mathematica Bohemica, Tome 118 (1993) no. 3, pp. 225-240. doi: 10.21136/MB.1993.125928
@article{10_21136_MB_1993_125928,
     author = {Vala, Josef},
     title = {Grassmann manifold $V\sp 4\sb 3$ in the projective space $P\sb 7$ with characteristics consisting of a quadric and two planes},
     journal = {Mathematica Bohemica},
     pages = {225--240},
     year = {1993},
     volume = {118},
     number = {3},
     doi = {10.21136/MB.1993.125928},
     mrnumber = {1239117},
     zbl = {0854.53015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1993.125928/}
}
TY  - JOUR
AU  - Vala, Josef
TI  - Grassmann manifold $V\sp 4\sb 3$ in the projective space $P\sb 7$ with characteristics consisting of a quadric and two planes
JO  - Mathematica Bohemica
PY  - 1993
SP  - 225
EP  - 240
VL  - 118
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1993.125928/
DO  - 10.21136/MB.1993.125928
LA  - en
ID  - 10_21136_MB_1993_125928
ER  - 
%0 Journal Article
%A Vala, Josef
%T Grassmann manifold $V\sp 4\sb 3$ in the projective space $P\sb 7$ with characteristics consisting of a quadric and two planes
%J Mathematica Bohemica
%D 1993
%P 225-240
%V 118
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1993.125928/
%R 10.21136/MB.1993.125928
%G en
%F 10_21136_MB_1993_125928

[1] C. П. Фиников: Теория пар конгруенций. Mocквa, 1956. | Zbl

[2] Л. З. Крузляков: Основы проективно-дифференциальной геометрии семейства многомерных плоскостей. Toмсk, 1980. | Zbl

[3] A. Švec: Projective differential geometry of line congruences. Praha, 1956.

[4] J. Vala: Special Grassman manifold $V_3^4$ in the projective space $P_7$. Časopis pěst. mat. 113 (1988), 36-51. | MR

Cité par Sources :