Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 2
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Gelbukh, Irina 2018. Loops in Reeb Graphs of n-Manifolds. Discrete & Computational Geometry, Vol. 59, Issue. 4, p. 843.
    Babalic, Elena Mirela and Lazaroiu, Calin Iuliu 2015. Singular foliations for M-theory compactification. Journal of High Energy Physics, Vol. 2015, Issue. 3,
    ×
  • Access

ON COLLINEAR CLOSED ONE-FORMS

  • IRINA GELBUKH (a1)
Abstract

We study one-forms with zero wedge-product, which we call collinear, and their foliations. We characterise the set of forms that define a given foliation, with special attention to closed forms and forms with small singular sets. We apply the notion of collinearity to give a criterion for the existence of a compact leaf and to study homological properties of compact leaves.

    •
      • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      ON COLLINEAR CLOSED ONE-FORMS
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      ON COLLINEAR CLOSED ONE-FORMS
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      ON COLLINEAR CLOSED ONE-FORMS
      Available formats
      ×
Copyright
COPYRIGHT: © Australian Mathematical Publishing Association Inc. 2011
References
Hide All
[1]Arnoux, P. and Levitt, G., ‘Sur l’unique ergodicité des 1-formes fermées singulières’, Invent. Math. 84 (1986), 141–156.
[2]Ayón-Beato, E., García, A., Macías, A. and Quevedo, H., ‘Static black holes of metric-affine gravity in the presence of matter’, Phys. Rev. D 64 (2001), 024026.
[3]Bott, R. and Tu, L. W., Differential Forms in Algebraic Topology, Graduate Texts in Mathematics, 82 (Springer, New York, 1982).
[4]Farber, M., Topology of Closed One-forms, Mathematical Surveys, 108 (American Mathematical Society, Providence, RI, 2004).
[5]Farber, M., Katz, G. and Levine, J., ‘Morse theory of harmonic forms’, Topology 37(3) (1998), 469–483.
[6]Ferrando, J. J. and Sáez, J. A., ‘Type I vacuum solutions with aligned Papapetrou fields: an intrinsic charactrization’, J. Math. Phys. 47 (2006), 112501.
[7]Gelbukh, I., ‘Presence of minimal components in a Morse form foliation’, Differential Geom. Appl. 22 (2005), 189–198.
[8]Gelbukh, I., ‘Number of minimal components and homologically independent compact leaves for a Morse form foliation’, Studia Sci. Math. Hungar. 46(4) (2009), 547–557.
[9]Gelbukh, I., ‘On the structure of a Morse form foliation’, Czechoslovak Math. J. 59(1) (2009), 207–220.
[10]Gelbukh, I., ‘Ranks of collinear Morse forms’, J. Geom. Phys. 61(2) (2011), 425–435.
[11]Hehl, F. W. and Socorro, J., ‘Gauge theory of gravity: electrically charged solutions within the metric-affine framework’, Acta Phys. Polon. B 29 (1998), 1113–1120.
[12]Hurewicz, W. and Wallman, H., Dimension Theory (Princeton University Press, Princeton, NJ, 1996).
[13]Kahn, D. W., Introduction to Global Analysis, Pure and Applied Mathematics, 91 (Academic Press, New York, 1980).
[14]Mel’nikova, I., ‘A test for compactness of a foliation’, Math. Notes 58(6) (1995), 1302–1305.
[15]Mel’nikova, I., ‘Singular points of a Morsian form and foliations’, Moscow Univ. Math. Bull. 51(4) (1996), 33–36.
[16]Mel’nikova, I., ‘Noncompact leaves of foliations of Morse forms’, Math. Notes 63(6) (1998), 760–763.
[17]Mel’nikova, I., ‘Maximal isotropic subspaces of skew-symmetric bilinear mapping’, Moscow Univ. Math. Bull. 54(4) (1999), 1–3.
[18]Mulay, S. B., ‘Cycles and symmetries of zero-divisors’, Comm. Algebra 30 (2002), 3533–3558.
[19]Sacksteder, R., ‘Foliations and pseudo-groups’, Amer. J. Math. 87 (1965), 79–102.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×
MathJax

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 45 *
Loading metrics...

Abstract views

Total abstract views: 92 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 16th August 2018. This data will be updated every 24 hours.

Cancel
Confirm
×