University of Mohaghegh Ardabili Journal of Hyperstructures 2251-8436 6 1 2017 06 01 Hypersurfaces in the general inner product spaces 17 27 2658 10.22098/jhs.2017.2658 EN Ali Parsian Department of Mathematics, Tafresh University, Tafresh 39518 79611, Iran Journal Article 2016 08 30 Let A be a symmetric positive definite (n+ 1)×(n+ 1) real matrix for n ≥ 1 and S ∈ R n+1 be a hypersurface. We are supposed to determine the tangent space TpS in an arbitrary point p ∈ S in the case that the whole space R n+1 admits the inner product with matrix A. Among other things, some maximum and minimum properties for the vector fields perpendicular to tangent spaces of hypersurfaces, the compatibility of the image or inverse image of a hypersurface and its tangent space under an embedding, an isometry, and a submersion are also pointed out.  https://jhs.uma.ac.ir/article_2658_afd0f6b6b3590bf3220a590d0d260586.pdf