We consider non-degenerate graph immersions into affine space An+1 whose cubic form is parallel with respect to the Levi-Civita connection of metric. There exists a correspondence between such and pairs (J,?), where J an n-dimensional real Jordan algebra ? trace on J. Every immersion can be extended complete symmetric covering maximal connected component zero in set quasi-regular elements It im...

We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, SU(2)-structures on 5-manifolds defined by a generalized Killing spinor. We prove that in the real analytic case, such a 5-manifold can be isometrically embedded as a hypersurface in a Calabi-Yau manifold in a natural way. We classify nilmanifolds carrying invariant structures of th...

It is shown that for a wide class of analytic Lagrangians which depend only on the scalar curvature of a metric and a connection, the application of the so–called “Palatini formalism”, i.e., treating the metric and the connection as independent variables, leads to “universal” equations. If the dimension n of space–time is greater than two these universal equations are Einstein equations for a g...

In this paper, we review the algebraic properties of various nonArchimedean ordered structures, extending them in various steps which lead naturally to the smallest non-Archimedean ordered field that is Cauchy-complete and real closed. In fact, the Levi-Civita field is small enough to allow for the calculus on the field to be implemented on a computer and used in applications such as the fast a...

A detailed study of power series on the Levi-Civita fields is presented. After reviewing two types of convergence on those fields, including convergence criteria for power series, we study some analytical properties of power series. We show that within their domain of convergence, power series are infinitely often differentiable and reexpandable around any point within the radius of convergence...

Article history: Received 22 June 2009 Available online 19 February 2010 Submitted by B. Sims

We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, SU(2)-structures on 5manifolds defined by a generalized Killing spinor. We prove that in the real analytic case, such a 5-manifold can be isometrically embedded as a hypersurface in a Calabi-Yau manifold in a natural way. We classify nilmanifolds carrying invariant structures of thi...

In this paper, we study connections on hermitian modules, and show that metric exist regular modules; i.e. finitely generated projective modules together with a non-singular form. addition, develop an index calculus for such provide characterization in terms of the existence pseudo-inverse matrix representing form respect to set generators. As first illustration above concepts, find fuzzy spher...

We extend to the spatial case a technique of integration close encounters formulated by Tullio Levi-Civita for planar restricted three-body problem. consider Hamiltonian introduced in Kustaanheimo-Stiefel regularization and construct complete integral related Hamilton-Jacobi equation means series convergent neighbourhood collisions with primary or secondary body.