There is no one to one 1-Lipschitz function from S2 to the interval [0,1] because of 1.2. Is there finite to one 1-Lipschitz function from S2 to the interval [0,1]? Is there countable to one 1-Lipschitz fuction from S2 to the interval [0,1]? The answers are no for both questions becase of 5.3. In this paper, I define a family of new metrics on the Euclidean 2-sphere of radius r in which the dis...

Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.

a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...

In this paper, a technique for analyzing levels of hierarchy in a tiling T of Euclidean space is presented. Fixing a central configuration P of tiles in T , a “derived Voronöı” tessellation TP is constructed based on the locations of copies of P in T . A family of derived Voronöı tilings F(T ) is formed by allowing the central configurations to vary through an infinite number of possibilities. ...

We study the space of all extensions of a real hyperplane arrangement by a new pseudo-hyperplane, and, more generally, of an oriented matroid by a new element. The question whether this space has the homotopy type of a sphere is a special case of the “Generalized Baues Problem” of Billera, Kapranov & Sturmfels, via the Bohne-Dress Theorem on zonotopal tilings. We prove that the extension space ...