Six-dimensional space is any space that has six dimensions, six degrees of freedom, and that needs six pieces of data, or coordinates, to specify a location in this space. There are an infinite number of these, but those of most interest are simpler ones …

In mathematics, an n-sphere or hypersphere is an ⁠ ⁠ - dimensional generalization of the ⁠ ⁠ -dimensional circle and ⁠ ⁠ -dimensional sphere to any non-negative integer ⁠ ⁠.

In geometry, a ball is a region in a space comprising all points within a fixed distance, called the radius, from a given point; that is, it is the region enclosed by a sphere or hypersphere. An n -ball is a ball in an n -dimensional Euclidean space.

May 27, 2018 · In [1] I gave a proof of the long-standing conjecture that the 6-dimensional sphere has no complex structure. In this paper I will present the proof in a more transparent manner. I use the example of the 6-sphere to shed new light on many problems of physics.

Abstract In [1] I gave a proof of the long-standing conjecture that the 6-dimensional sphere has no complex structure. In this paper I will present the proof in a more trans-parent manner. I use the example of the 6-sphere to shed new light on many problems of physics.

Apr 8, 2025 · Moon, P. and Spencer, D. E. "6-Sphere Coordinates ." Fig. 4.07 in Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions, 2nd ed. New York: Springer-Verlag, pp. 122-123, 1988.

We show the non-existence of complex structure on sphere with the standard round metric, of any dimension other than two, in particular, on $S^6$. We review some of the most remarkable results obtained by Ya.G. Sinai and collaborators on the difficult problems arising in the theory of the Navier– Stokes equations and related models. The survey…

Nov 1, 2016 · The argument that there is no orthogonal complex structure on the 6-sphere is due to Claude Lebrun and the point is that such a thing, viewed as a section of twistor space, has as image a complex submanifold.

Jul 18, 2024 · The 6-sphere, as a smooth manifold is diffeomorphic to the coset space S 6 ≃ G 2 / SU ( 3 ) S^6 \simeq G_2/ SU(3) of G₂ ( automorphism group of the octonions ) by SU(3) ( Fukami-Ishihara 55 ).

Nov 16, 2022 · We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn-Triantafillou to the case of odd weight and non-trivial character. Bibliographic Explorer (What is the Explorer?)