Describing shapes by suitable measures in object segmentation, as proposed in [24], allows to combine the advantages of the representations as parametrized contours and indicator functions. The pseudo-Riemannian structure of optimal transport can be used to model shapes in ways similar as with contours, while the Kantorovich functional enables the application of convex optimization methods for ...

I show that all FRW models (four dimensional pseudo-Riemannian manifolds with maximally symmetric space) can be embedded in a flat Minkowski manifold with 5 dimensions. The pseudo Riemannian metric of space-time is induced by the flat metric. This generalizes the usual embedding widely used for the de Sitter models. I give the coordinate transformations for the embedding. Taking into account th...

In the first part of this paper, some theorems are given for a Riemannian manifold with semi-symmetric metric connection. In the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. We obtain some properties of this manifold having the vectors mentioned above.

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...

The present paper discusses the problem of least-squares over the real symplectic group of matrices Sp(2n,R). The least-squares problem may be extended from flat spaces to curved spaces by the notion of geodesic distance. The resulting non-linear minimization problem on manifold may be tackled by means of a gradient-descent algorithm tailored to the geometry of the space at hand. In turn, gradi...

Pseudo-parallel (shortly PP) submanifolds are defined as a generalization of semi-parallel (shortly SP ) submanifolds and as extrinsic analogue of pseudo-symmetric (shortly PS) manifolds (in the sense of R. Deszcz) [1], [26]. Asperti et al [1] obtained a description of PP hypersurfaces in space form as quasiumbilic hypersurfaces or cyclids of Dupin and studied PP surfaces with maximal first nor...

A basic question, first addressed by A. Lichnerowicz, is to characterize the pseudo-Riemannian manifolds (M,σ) for which Conf M does not preserve any metric in [σ]; in this case, Conf M is essential. The Lichnerowicz conjecture, proved by J. Lelong-Ferrand [LF1], says, for (M,σ) a Riemannian manifold of dimension ≥ 2, if Conf M is essential, then M is conformally equivalent to the round sphere ...

the present article serves the purpose of pursuing geometrization of heat flow on volumetrically isothermal manifold by means of rf approach. in this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of riemannian manifold and fundamental properties of thermodynamic systems. by making use of the notions of various curva...

In this paper, we investigate geodesics of the tangent bundle $TM$ a Riemannian manifold $(M,g)$ endowed with an arbitrary pseudo-Riemannian $g$-natural metric Kaluza-Klein type. Then considering class naturally defined almost complex structures on $TM$, constructed by V. Oproiu, construct magnetic fields and characterize corresponding curves when is space form.