Non-associative geometry and discrete structure of spacetime
A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.
A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.
We obtain upper and lower estimates for the Green function for a second order noncoercive differential operator on a homogeneous manifold of negative curvature.
We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riemannian manifold and of its a non-degenerate hypersurface with respect to a semi-symmetric metric connection....
For a vector bundle functor with the point property we prove that is product preserving if and only if for any and there is an -natural operator transforming connections on -dimensional fibered manifolds into connections on . For a bundle functor with some weak conditions we prove non-existence of -natural operators transforming connections on -dimensional fibered manifolds into connections on .
We extend a construction by K. Yamato [Ya] to obtain new explicit examples of Riemannian 3-manifolds as in the title. Some of these examples have an interesting geometrical interpretation.