Related papers: Five-Dimensional Tangent Vectors in Space-Time
The presence of defects in material continua is known to produce internal permanent strained states. Extending the theory of defects to four dimensions and allowing for the appropriate signature, it is possible to apply these concepts to…
Angular momentum is traditionally taught as a (pseudo)vector quantity, tied closely to the cross product. This approach is familiar to experts but challenging for students, and full of subtleties. Here, we present an alternative pedagogical…
In five dimensional cosmological models, the convention is to include the fifth dimension in a way similar to the other space dimensions. In this work we attempt to introduce the fifth dimension in a way that a time dimension would be…
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
The explicit coordinate transformations which show the equivalence between a four-dimensional spatially flat cosmology and an appropriate submanifold in the flat five-dimensional Minkowski space-time are presented. Analogous procedure is…
A tangent category is a category equipped with an endofunctor that satisfies certain axioms which capture the abstract properties of the tangent bundle functor from classical differential geometry. Cockett and Cruttwell introduced…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
A unification model for strong, electromagnetic, weak and gravitational forces is proposed. The tangent space of ordinary coordinate 4-dimensional spacetime is a submanifold of an 14-dimensional internal spacetime spanned by four frame…
An attempt to get a non-trivial-mass structure of particles in a Randall-Sundrum type of 5-dimensional spacetime with q-deformed extra dimension is discussed. In this spacetime, the fifth dimensional space is boundary free, but there…
Eigenvectors of stress-energy tensor (the source in Einstein's equations) form privileged bases in description of the corresponding space-times. When one or more of these vector fields are rotating (the property well determined in…
A generalized scalar-tensor theory is investigated whose cosmological term depends on both a scalar field and its time derivative. A correspondence with solutions of five-dimensional Space-Time-Matter theory is noted. Analytic solutions are…
We construct the tensor hierarchies of generic, bosonic, 5- and 6-dimensional field theories. The construction of the tensor hierarchy starts with the introduction of two tensors: the embedding tensor which tells us which vector is used for…
We consider a relation between local and global characteristics of a differential algebraic variety. We prove that dimension of tangent space for every regular point of an irreducible differential algebraic variety coincides with dimension…
This paper constructs the geometrically natural objects which are associated with any projection tensor field on a manifold with any affine connection. The approaches to projection tensor fields which have been used in general relativity…
It is shown that if a generalized definition of gauge invariance is used, gauge invariant effective stress-energy tensors for gravitational waves and other gravitational perturbations can be defined in a much larger variety of circumstances…
In this paper, we have considered a 5-dimensional warped product space-time with a timedependent warp factor. The time-dependent warp factor plays an important role in localizing matter to the 4-dimensional hypersurface constituting the…
Einstein-Gauss-Bonnet gravity in five-dimensional spacetime provides an excellent example of a theory that, while including higher-order curvature corrections to General Relativity, still shares many of its features, such as second-order…
A Clifford Space is counted to be a tempting approach to unify both micro-physics and macro-physics simultaneously. Such a tendency may be found in the realm of replacing vectors with poly-vectors. Accordingly, the problem of motion becomes…
The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate…
This paper explores a new perspective on the universality of the vertical lift in tangent categories by presenting a categorification of the dimension of smooth manifolds. The universality of the vertical lift is a key part of the axioms of…