Geometry of Four-Vector Fields on Quaternionic Flag Manifolds

Philip Foth; Frederick Leitner

doi:10.1007/s00220-003-0821-9

Geometry of Four-Vector Fields on Quaternionic Flag Manifolds

Communications in Mathematical Physics ◽

10.1007/s00220-003-0821-9 ◽

2003 ◽

Vol 238 (1) ◽

pp. 119-129

Author(s):

Philip Foth ◽

Frederick Leitner

Keyword(s):

Vector Fields ◽

Flag Manifolds

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Vector fields on real flag manifolds

Annals of Global Analysis and Geometry ◽

10.1007/bf01000338 ◽

1985 ◽

Vol 3 (2) ◽

pp. 173-184 ◽

Cited By ~ 3

Author(s):

Július Korbaš

Keyword(s):

Vector Fields ◽

Flag Manifolds

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Vector fields on the real flag manifolds ℝF(1, 1, n − 2)

Mathematica Slovaca ◽

10.2478/s12175-007-0060-1 ◽

2008 ◽

Vol 58 (1) ◽

Cited By ~ 1

Author(s):

Samuel Ilori ◽

Deborah Ajayi

Keyword(s):

Vector Fields ◽

Flag Manifolds ◽

The Real

AbstractWe obtain the span of the real flag manifolds ℝF(1, 1, n−2), n ≥ 3, for the cases n ≡ 2 (mod 4), n ≡ 4 (mod 8) and n ≡ 8 (mod 16) and use the results to deduce that certain Stiefel-Whitney classes of the manifold are zero.

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ON GRÖBNER BASES FOR FLAG MANIFOLDS F(1, 1, … , 1, n)

Journal of Algebra and Its Applications ◽

10.1142/s0219498812501824 ◽

2012 ◽

Vol 12 (03) ◽

pp. 1250182

Author(s):

ZORAN Z. PETROVIĆ ◽

BRANISLAV I. PRVULOVIĆ

Keyword(s):

Vector Fields ◽

Polynomial Algebra ◽

Gröbner Bases ◽

Flag Manifold ◽

Grobner Bases ◽

Flag Manifolds ◽

Embedding Dimension ◽

The Real ◽

Real Flag Manifold ◽

Complete Flag

The knowledge of cohomology of a manifold has shown to be quite relevant in various investigations: the question of vector fields, immersion and embedding dimension, and recently even in topological robotics. The method of Gröbner bases is applicable when the cohomology of the manifold is a quotient of a polynomial algebra. The mod 2 cohomology of the real flag manifold F(n1, n2, …, nr) is known to be isomorphic to a polynomial algebra modulo a certain ideal. Reduced Gröbner bases for these ideals are obtained in the case of manifolds F(1, 1, …, 1, n) including the complete flag manifolds (n = 1).

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