Orthogonal Projections Based on Hyperbolic and Spherical n-Simplex

In this paper, orthogonal projection along a geodesic to the chosen k-plane is introduced using edge and Gram matrix of an n-simplex in hyperbolic or spherical n-space. The distance from a point to k-plane is obtained by the orthogonal projection. It is also given the perpendicular foots from a point to k-plane of hyperbolic and spherical n-space.Comment: 13 page

Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

WOS: 000247678600010Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces

On the Schlafli differential formula based on edge lengths of tetrahedron in H-3 and S-3

WOS: 000262124300007We obtain a new version of Schlafli differential formula based on edge lengths for the volume of a tetrahedron in hyperbolic and spherical 3-spaces, by using the edge matrix of a hyperbolic( or spherical) tetrahedron and its submatrix

Orthogonal Projections Based on Hyperbolic and Spherical n-Simplex

Orthogonal projection along a geodesic to the chosen k-plane is introduced using edge and Gram matrix of an n-simplex in hyperbolic or spherical n-space. The distance from a point to k-plane is obtained by the orthogonal projection. It is also given the perpendicular foot from a point to k-plane of hyperbolic and spherical n-space