Axioms, Vol. 15, Pages 146: Intrinsic and Extrinsic Geometry of Pseudoparallel Submanifolds in Almost Kenmotsu (κ,μ,ν)-Manifolds

Axioms doi: 10.3390/axioms15020146

Authors:
Ibrahim Al-Dayel
Tuğba Mert
Mohd Danish Siddiqi

In this paper, we undertake a detailed study of pseudoparallel submanifolds of almost Kenmotsu (κ,μ,ν)-spaces, with particular emphasis on invariant submanifolds. By employing the W0 and W1 curvature tensors, we analyze several classes of pseudoparallel submanifolds, including Ricci-generalized pseudoparallel ones, and investigate how these curvature conditions influence the intrinsic and extrinsic geometry of the submanifolds. One of the main contributions of this work is the derivation of necessary and sufficient conditions under which invariant pseudoparallel submanifolds of almost Kenmotsu (κ,μ,ν)-spaces become totally geodesic. In particular, the use of the W0 and W1 curvature tensors provides a unified and effective framework for characterizing total geodesicity in this geometric setting. Furthermore, we obtain new and significant classification results by explicitly relating the total geodesicity of invariant submanifolds to the structural functions κ,μ and ν. These results not only generalize several known characterizations in the literature but also yield novel geometric insights into the structure of pseudoparallel submanifolds in almost Kenmotsu (κ,μ,ν)-spaces. We also provide an example to support our concept.

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