Second Order parallel tensor on generalized f.pk-space form and hypersurfaces of generalized f.pk-space form

TL;DR

This paper investigates the existence and properties of second order symmetric parallel tensors and hypersurfaces in generalized f.pk-space forms, establishing non-existence results for certain tensors and hypersurfaces.

Contribution

It characterizes second order symmetric parallel tensors in generalized f.pk-space forms and proves the non-existence of parallel hypersurfaces in this setting.

Findings

No second order skew-symmetric parallel tensors exist in f.pk-space form.

No parallel hypersurfaces exist in generalized f.pk-space form.

Semi-parallel hypersurfaces can exist in generalized f.pk-space form.

Abstract

The purpose of the present paper to study a second order symmetric parallel tensor in generalized f.pk-space form. Second order symmetric parallel tensor in f.pk-space form is combination of the associated metric tensor and $1$-forms of structure vector fields. We prove that there does not exist second order skew-symmetric parallel tensor in f.pk-space form. We also deduce that there is no parallel hypersurface in a generalized f.pk-space form but there is semi-parallel hypersurfaces in a generalized f.pk-space form.