Grassmann manifold V 3 4 in the projective space P 7 with characteristics consisting of a quadric and two planes

Josef Vala

Mathematica Bohemica (1993)

  • Volume: 118, Issue: 3, page 225-240
  • ISSN: 0862-7959

Abstract

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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 3 4 with characteristics consisting of a quadric and two planes are studied. The properties of the manifold dual to V 3 4 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].

How to cite

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Vala, Josef. "Grassmann manifold $V^4_3$ in the projective space $P_7$ with characteristics consisting of a quadric and two planes." Mathematica Bohemica 118.3 (1993): 225-240. <http://eudml.org/doc/29082>.

@article{Vala1993,
abstract = {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].},
author = {Vala, Josef},
journal = {Mathematica Bohemica},
keywords = {systems of linear spaces; dual manifold; four-parametric manifolds; projective space; characteristics; differential geometry of systems of linear spaces; systems of linear spaces; dual manifold; four-parametric manifolds; projective space; characteristics},
language = {eng},
number = {3},
pages = {225-240},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Grassmann manifold $V^4_3$ in the projective space $P_7$ with characteristics consisting of a quadric and two planes},
url = {http://eudml.org/doc/29082},
volume = {118},
year = {1993},
}

TY - JOUR
AU - Vala, Josef
TI - Grassmann manifold $V^4_3$ in the projective space $P_7$ with characteristics consisting of a quadric and two planes
JO - Mathematica Bohemica
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 118
IS - 3
SP - 225
EP - 240
AB - 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].
LA - eng
KW - systems of linear spaces; dual manifold; four-parametric manifolds; projective space; characteristics; differential geometry of systems of linear spaces; systems of linear spaces; dual manifold; four-parametric manifolds; projective space; characteristics
UR - http://eudml.org/doc/29082
ER -

References

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  1. C. П. Фиников, Теория пар конгруенций, Mocквa, 1956. (1956) Zbl0995.90522
  2. Л. З. Крузляков, Основы проективно-дифференциальной геометрии семейства многомерных плоскостей, Toмсk, 1980. (1980) Zbl1138.81416
  3. A. Švec, Projective differential geometry of line congruences, Praha, 1956. (1956) 
  4. J. Vala, Special Grassman manifold V 3 4 in the projective space P 7 , Časopis pěst. mat. 113 (1988), 36-51. (1988) MR0930804

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