Lata Bisht1, Sandhana Shanker2
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Scope of this paper is to express the Nijenhius Tensor in various forms in Hyperbolic Hsu-Structure manifold. Firstly Hyperbolic Hsu-Structure manifold has been studied and discussed by Dr. R.S. Mishra ,  and some of the great geometricians have also done work in Nijenhius Tensor in different differentiable manifold structures , , , . In this paper, we have taken even dimensional differentiable manifold Vn(n = 2m) of differentiability class C ∞, where we have definedthe Nijenhius Tensor in Hyperbolic Hsu-Structure manifold and the decomposition of the Nijenhius Tensor in Hyperbolic Hsu-Structure has been done. And some of its properties have also been discussed. Similarly the decomposition of the associate Nijenhius Tensor and its properties in Hyperbolic Hsu-structure manifold has been discussed.
|Hyperbolic- Hsu structure manifold, Nijenhius Tensor, HGF-structure|
|Proof: Interchanging X and Y in equation (2.1b), we get (2.2a), which shows that N is Skew-Symmetric in X and Y. Barring equation (2.1b) and applying structure we get equation (2.2c). Barring X and Y separately in equation (2.1b) and using structure in the two equations and then comparing the resulting equation we get (2.2b). Barring equation (2.2b) throughout and using structure in the resulting equation, we get the equation (2.2d). Barring X and Y in equation (2.1b), using structure and comparing the resulting equation with the equation obtained by multiplying equation (2.1b) by we get the equation (2.2e), which shows that N is pure in X and Y. Barring equation (2.2e)and using structure, we get the equation (2.2f). The equation (1.3a) is obtained from the equations (2.2d) and (2.2e). The equation (2.2c) and (2.2f) yield the equation (2.3b).|
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