Some applications of Bochner formula to submanifolds of a unit sphere

2011 ◽  
Vol 78 (3-4) ◽  
pp. 625-631
Author(s):  
GUOXIN WEI
Keyword(s):  
Unit Sphere ◽  
Bochner Formula

scholarly journals Generalised Kochen–Specker Theorem in Three Dimensions

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Václav Voráček ◽  
Mirko Navara
Keyword(s):  
Unit Sphere ◽  
Hidden Variables ◽  
Three Dimensions ◽  
Quantum Theories

AbstractWe show that there is no non-constant assignment of zeros and ones to points of a unit sphere in $$\mathbb{R}^3$$ R 3 such that for every three pairwisely orthogonal vectors, an odd number of them is assigned 1. This is a new strengthening of the Bell–Kochen–Specker theorem, which proves the non-existence of hidden variables in quantum theories.

Unit Sphere-Constrained and Higher Order Interpolations in Laplace’s Method of Initial Orbit Determination

2019 ◽  
Vol 67 (3) ◽  
pp. 1116-1138
Author(s):  
Ethan R. Burnett ◽  
Andrew J. Sinclair ◽  
Carolyn C. Fisk
Keyword(s):  
Unit Sphere ◽  
Orbit Determination ◽  
Higher Order ◽  
Laplace’S Method ◽  
Initial Orbit Determination ◽  
Laplace's Method ◽  
Initial Orbit

scholarly journals Optimal logarithmic energy points on the unit sphere

2008 ◽  
Vol 77 (263) ◽  
pp. 1599-1613 ◽  
Author(s):  
J. S. Brauchart
Keyword(s):  
Unit Sphere ◽  
Logarithmic Energy

Vertex Subgroups of Irreducible Representations of Solvable Groups

1971 ◽  
Vol 23 (1) ◽  
pp. 12-21
Author(s):  
J. Malzan
Keyword(s):  
Vector Space ◽  
Unit Sphere ◽  
Convex Subset ◽  
Orthogonal Group ◽  
Solvable Groups ◽  
Fundamental Region ◽  
Irreducible Representations ◽  
Theoretical Problem ◽  
Real Vector ◽  
The Real

If ρ(G) is a finite, real, orthogonal group of matrices acting on the real vector space V, then there is defined [5], by the action of ρ(G), a convex subset of the unit sphere in V called a fundamental region. When the unit sphere is covered by the images under ρ(G) of a fundamental region, we obtain a semi-regular figure.The group-theoretical problem in this kind of geometry is to find when the fundamental region is unique. In this paper we examine the subgroups, ρ(H), of ρ(G) with a view of finding what subspace, W of V consists of vectors held fixed by all the matrices of ρ(H). Any such subspace lies between two copies of a fundamental region and so contributes to a boundary of both. If enough of these boundaries might be found, the fundamental region would be completely described.

scholarly journals Towards the fixed point property for superreflexive spaces

2001 ◽  
Vol 64 (3) ◽  
pp. 435-444 ◽  
Author(s):  
Andrzej Wiśnicki
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Unit Sphere ◽  
Convex Set ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
Geometrical Condition

A Banach space X is said to have property (Sm) if every metrically convex set A ⊂ X which lies on the unit sphere and has diameter not greater than one can be (weakly) separated from zero by a functional. We show that this geometrical condition is closely connected with the fixed point property for nonexpansive mappings in superreflexive spaces.

On the Stationary Values of a Fourth-Degree Polynomial on the Unit Sphere

1970 ◽  
Vol 18 (3) ◽  
pp. 580-583 ◽  
Author(s):  
William L. Morris
Keyword(s):  
Unit Sphere ◽  
Degree Polynomial ◽  
Fourth Degree

scholarly journals Complete Riemannian manifold minimally immersed in a unit sphere $S^{n+p} (1)$

1989 ◽  
Vol 13 (1) ◽  
pp. 107-112 ◽  
Author(s):  
Qing-ming Cheng ◽  
Yuen-da Wang
Keyword(s):  
Riemannian Manifold ◽  
Unit Sphere ◽  
Complete Riemannian Manifold
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