Nullity Distributions Associated with Hashiguchi Connection

Soleiman, A.; Elgendi, S. G.

doi:10.28924/2291-8639-23-2025-184

Research Article

Nullity Distributions Associated with Hashiguchi Connection

A. Soleiman
S. G. Elgendi*

* Corresponding author

Abstract

In this paper, we employ the Klein-Grifone formalism to study the nullity distributions associated with the curvature tensors of the Hashiguchi connection. We establish several important results regarding the nullity distribution \(\mathcal{N}_{R^\star}\) of the h-curvature tensor \(\overset{*}{R}\), demonstrating that \(\mathcal{N}_{R^\star}\) is completely integrable and that its corresponding foliation consists of auto-parallel leaves. An illustrative example shows that the nullity distribution \(\mathcal{N}_{P^\star}\), associated with the hv-curvature tensor \(\overset{*}{P}\), is not generally completely integrable. Furthermore, we determine necessary and sufficient conditions under which \(\mathcal{N}_{P^\star}\) becomes completely integrable.

How to Cite

A. Soleiman, S. G. Elgendi, Nullity Distributions Associated with Hashiguchi Connection, Int. J. Anal. Appl. 23 (2025), 184. https://doi.org/10.28924/2291-8639-23-2025-184

BibTeX

@article{Soleiman2025,
  author  = {Soleiman, A. and Elgendi, S. G.},
  title   = {Nullity Distributions Associated with Hashiguchi Connection},
  journal = {Int. J. Anal. Appl.},
  volume  = {23},
  year    = {2025},
  pages   = {184},
  doi     = {10.28924/2291-8639-23-2025-184}
}

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