eng Ansari Education and Research Society Journal of Ultra Scientist of Physical Sciences December 2009 21 3 954 956 jusps-A 1282 article SHANKAR LAL 1 MANOJ SEMALTYu00a0 1 Department of Mathematics, H.N.B., Garhwal University, (A Central University). S.R.T.., Campus, Badshaithaul (Tehri Garhwal- 249199 Uttarakhand (INDIA) <p style="text-align: justify;">The aim of the present paper, we have studied almost hyperbolic Hermite manifolds and also obtain a few interesting results. Almost contact hyperbolic (<em>f,g,h,x</em>) structures have been defined by M.D. Upadhyay and K.K. Dube⁷&nbsp;and others. Vanzara⁸&nbsp;studied almost r-contact structures. The paper is organized as fallows. Section1, contains a brief introduction to hyperbolic Hermite and Nijenhuis tensor, while in section 2 some necessary details about some results of manifolds are presented. In section 3, we define affine connections of&nbsp;<em>D</em>&nbsp;in mⁿ&nbsp;and a vector valued bilinear function of torsion tensor.</p> https://www.ultrascientist.org/paper/1282/ Riemannian metric hyperbolic Hermite manifold Nijenhuis tensor torsion tensor affine connection.