Decomposition in the large of two-forms of constant rank

Ibrahim Dibag

Annales de l'institut Fourier (1974)

  • Volume: 24, Issue: 3, page 317-335
  • ISSN: 0373-0956

Abstract

top
The purpose of this paper is to find necessary and sufficient conditions for globally-decomposing an exterior 2-form w , of constant rank 2 s , on a vector-bundle E , as a sum : w = y 1 ∧ y s + 1 + ⋯ + y s ∧ y 2 s . The general theory is applied to low dimensional manifolds, spheres, real and complex projective spaces.

How to cite

top

Dibag, Ibrahim. "Decomposition in the large of two-forms of constant rank." Annales de l'institut Fourier 24.3 (1974): 317-335. <http://eudml.org/doc/74189>.

@article{Dibag1974,
abstract = {The purpose of this paper is to find necessary and sufficient conditions for globally-decomposing an exterior 2-form $w$, of constant rank $2s$, on a vector-bundle $E$, as a sum :\begin\{\}w=y\_1\wedge y\_\{s+1\}+\cdots +y\_s\wedge y\_\{2s\}.\end\{\}The general theory is applied to low dimensional manifolds, spheres, real and complex projective spaces.},
author = {Dibag, Ibrahim},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {317-335},
publisher = {Association des Annales de l'Institut Fourier},
title = {Decomposition in the large of two-forms of constant rank},
url = {http://eudml.org/doc/74189},
volume = {24},
year = {1974},
}

TY - JOUR
AU - Dibag, Ibrahim
TI - Decomposition in the large of two-forms of constant rank
JO - Annales de l'institut Fourier
PY - 1974
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 3
SP - 317
EP - 335
AB - The purpose of this paper is to find necessary and sufficient conditions for globally-decomposing an exterior 2-form $w$, of constant rank $2s$, on a vector-bundle $E$, as a sum :\begin{}w=y_1\wedge y_{s+1}+\cdots +y_s\wedge y_{2s}.\end{}The general theory is applied to low dimensional manifolds, spheres, real and complex projective spaces.
LA - eng
UR - http://eudml.org/doc/74189
ER -

References

top
  1. [1] A. BOREL, Sur La Cohomologie des Espaces Fibre Principaux..., Ann. Math., 57 (1953), 115-207. Zbl0052.40001MR14,490e
  2. [2] A. BOREL, F. HIRZEBRUCH, Characteristic Classes and Homogenous Spaces I, Amer. J. Math., 80 (1958), 459-538. Zbl0097.36401
  3. [3] J. MARTINET, Sur Les Singularités des Formes Differentiables, Thesis Grenoble (1969). 
  4. [4] W.S. MASSEY, Obstructions to the Existence of Almost-Complex Structures, Bull. Amer. Math. Soc, 67 (1961), 559-564. Zbl0192.29601MR24 #A2971
  5. [5] C.E. MILLER, The Topology of Rotation Groups, Ann. Math, 57 (1953), 91-114. Zbl0050.17503MR14,673b
  6. [6] MOSHER-TANGORA, Cohomology Operations and Application in Homotopy Theory, Harper-Row Publishers (1968). Zbl0153.53302
  7. [7] N.E. STEENROD, The Topology of Fibre-Bundles, Princeton Univ. Press (1951). Zbl0054.07103MR12,522b
  8. [8] N.E. STEENROD, Cohomology Operations, Annals of Math Studies, n° 50. Zbl0102.38104MR26 #3056
  9. [9] S. STERNBERG, Lectures on Differential Geometry, Prentice Hall Edition (1964). Zbl0129.13102MR33 #1797
  10. [10] E. THOMAS, Complex-Structures on Real Vector-Bundles, Amer. J. Math., 89 (1967), 887-907. Zbl0174.54802MR36 #3375

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.