Geodesics and Deformed Pseudo–riemannian Manifolds with Symmetry
نویسنده
چکیده
There is a general method, applicable in many situations, whereby a pseudo–Riemannian metric, invariant under the action of some Lie group, can be deformed to obtain a new metric whose geodesics can be expressed in terms of the geodesics of the old metric and the action of the Lie group. This method applied to Euclidean space and the unit sphere produces new examples of complete Riemannian metrics whose geodesics are expressible in terms of elementary functions.
منابع مشابه
A Geometry Preserving Kernel over Riemannian Manifolds
Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...
متن کاملCommutative curvature operators over four-dimensional generalized symmetric spaces
Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.
متن کاملDiscrete Geodesics and Cellular Automata
This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily specializes to metric spaces such as discretized pseudo-riemannian manifolds. It is effective: an algorithm for computing these geodesics naturally follows, which all...
متن کاملGallot-Tanno theorem for closed incomplete pseudo-Riemannian manifolds and application
In this article we extend the Gallot-Tanno theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over such a manifold admits a parallel symmetric 2-tensor then it is incomplete and has non zero constant curvature. An application of this result to the existence of metrics with distinct Levi-Civita connections but having the same unparametrized geodesics is given.
متن کاملON THE LIFTS OF SEMI-RIEMANNIAN METRICS
In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...
متن کامل