SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2013 / Cilt: 42 - Sayı: 3

ANTI-INVARIANT ? -RIEMANNIAN SUBMERSIONS FROM ALMOST CONTACT MANIFOLDS

Jae Won LEE
Pages
231–241
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also find necessary and sufficient conditions for a special anti-invariant ??-Riemannian submersion to be totally geodesic.Moreover, we obtain decomposition theorems for the total manifold ofsuch submersions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce anti-invariant ??-Riemannian submersions from almostcontact manifolds onto Riemannian manifolds.
📊
Key Findings & Data:We give an example,investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of suchsubmersions.
💡
Conclusion & Impact:We also find necessary and sufficient conditions for a special anti-invariant ??-Riemannian submersion to be totally geodesic.Moreover, we obtain decomposition theorems for the total manifold ofsuch submersions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

We introduce anti-invariant ??-Riemannian submersions from almostcontact manifolds onto Riemannian manifolds. We give an example,investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of suchsubmersions. We also find necessary and sufficient conditions for a special anti-invariant ??-Riemannian submersion to be totally geodesic.Moreover, we obtain decomposition theorems for the total manifold ofsuch submersions.

🔖

Cite This Article

LEE, J. W. (2022). ANTI-INVARIANT ? -RIEMANNIAN SUBMERSIONS FROM ALMOST CONTACT MANIFOLDS. Hacettepe Journal of Mathematics and Statistics, Cilt: 42 - Sayı: 3, 231–241. https://ajindex.com/articles/530450

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (13)

  1. Altafini, C. Redundant robotic chains on Riemannian submersions, IEEE Transactions on Robotics and Automation, 20(2), 335-340, 2004
  2. Blair, D. E. Contact manifold in Riemannian geometry,(Lecture Notes in Math., 509, Springer-Verlag, Berlin-New York, 1976)
  3. Baird, P., Wood, J. C. Harmonic Morphisms Between Riemannian Manifolds, (London Mathematical Society Monographs, 29, Oxford University Press, The Clarendon Press, Oxford, 2003)
  4. Chinea, C. Almost contact metric submersions, Rend. Circ. Mat. Palermo, 43(1), 89-104, 1985
  5. Eells, J., Sampson, J. H. Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86, 109-160, 1964
  6. Falcitelli, M., Ianus, S., Pastore, A. M. Riemannian Submersions and Related Topics, (World Scientific, River Edge, NJ, 2004)
  7. Gray, A. Pseudo-Riemannian almost product manifolds and submersion, J. Math. Mech., 16, 715-737, 1967
  8. Ianus, S., Pastore A. M. Harmonic maps on contact metric manifolds, Ann. Math. Blaise Pascal, 2(2), 43-53, 1995
  9. O'Neill, B. The fundamental equations of a submersion, Mich. Math. J.,13, 458-469, 1966
  10. Ponge, R. Reckziegel, H. Twisted products in pseudo-Riemannian geometry, Geom. Dedicata, 48(1), 15-25, 1993
  11. Sahin, B. Anti-invariant Riemannian submersions from almost hermitian manifolds, Cent. Eur. J. Math., 8(3), 437-447, 2010
  12. Sasaki, S., Hatakeyama, Y. On differentiable manifolds with contact metric structure, J. Math. Soc. Japan, 14, 249-271, 1961
  13. Watson, B. Almost Hermitian submersions, J. Differential Geometry, 11(1), 147-165, 1976.