On the Geometry of Conformal Anti-invariant $\xi^\perp-$ Submersions

Authors

  • Mehmet Akif Akyol Bingol University
  • Yılmaz Gündüzalp Dicle University

Keywords:

Almost contact metric manifold, conformal submersion, anti-invariant $\xi^\perp-$ Riemannian submersion, conformal anti-invariant $\xi^\perp-$submersion

Abstract

Lee [Anti-invariant $\xi^{\perp}-$ Riemannian submersions from almost contact manifolds, Hacettepe Journal of Mathematics and Statistic, 42(3), (2013), 231-241.] defined and studied anti-invariant $\xi^\perp-$ Riemannian submersions from almost contact manifolds.
The main goal of this paper is to consider conformal anti-invariant $\xi^\perp-$ submersions (it means the Reeb vector field $\xi$ is a horizontal vector field) from almost contact metric manifolds onto Riemannian manifolds as a generalization of anti-invariant $\xi^\perp-$ Riemannian submersions. More precisely, we obtain the geometries of the leaves of $\ker\pi_{*}$ and $(\ker\pi_{*})^\perp,$ including the integrability of the distributions, the geometry of foliations, some conditions related to totally geodesicness and harmonicty of the submersions. Finally, we show that there are certain product structures on the total space of a conformal anti-invariant $\xi^\perp-$ submersion.

Downloads

Published

2018-04-24

How to Cite

Akyol, M. A., & Gündüzalp, Y. (2018). On the Geometry of Conformal Anti-invariant $\xi^\perp-$ Submersions. International Journal of Maps in Mathematics, 1(1), 50–67. Retrieved from https://journalmim.com/index.php/journalMIM/article/view/4

Issue

Vol. 1 No. 1 (2018): International Journal of Maps in Mathematics

Section

Articles

License

The copyright to the article is transferred to body International Journal of Maps in Mathematics effective if and when the article is accepted for publication.

  • The copyright transfer covers the exclusive right to reproduce and distribute the article, including reprints, translations, photographic reproductions, microform, electronic form (offline, online) or any other reproductions of similar nature.
  • An author may make his/her article published by body International Journal of Maps in Mathematics available on his/her home page provided the source of the published article is cited and body International Journal of Maps in Mathematics is mentioned as copyright owner.
  • The author warrants that this contribution is original and that he/she has full power to make this grant. The author signs for and accepts responsibility for releasing this material on behalf of any and all co-authors. After submission of this agreement signed by the corresponding author, changes of authorship or in the order of the authors listed will not be accepted by body International Journal of Maps in Mathematics.