In this paper, we study Einstein warped product space with respect to semi symmetric metric connection. During establish some results on curvature, Ricci and scalar tensors connection second order the last section, investigate under what conditions, if $M$ is an nonpositive curvature compact base then simply a Riemannian space.

In this paper we study spherically symmetric metrics on a space in $\mathbb{R}^n$ with scalar and constant flag curvature also obtain families of type metrics. Many explicit examples are provided for Douglas curvature. Furthermore, new projectively flat Finsler given. We provide family which not type.

Riemannian manifolds with a Levi-Civita connection and constant Ricci curvature, or Einstein manifolds, were studied in the works of many mathematicians. This question has been most homogeneous case. In this direction, famous ones are results by D.V. Alekseevsky, M. Wang, V. Ziller, G. Jensen, H.Laure, Y.G. Nikonorov, E.D. Rodionov other At same time, studying little for case an arbitrary metri...

Static spherically symmetric solutions for conformal gravity in three dimensions are found. Black holes and wormholes are included within this class. Asymptotically the black holes are spacetimes of arbitrary constant curvature, and they are conformally related to the matching of different solutions of constant curvature by means of an improper conformal transformation. The wormholes can be con...

A method of Hurwitz-Radon Matrices (MHR) is proposed to be used in parametrization and interpolation of contours in the plane. Suitable parametrization leads to curvature calculations. Points with local maximum curvature are treated as feature points in object recognition and image analysis. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. The operator of Hurw...

An algebraic curvature tensor is called Osserman if the eigenvalues of the associated Jacobi operator are constant on the unit sphere. A Riemannian manifold is called conformally Osserman if its Weyl conformal curvature tensor at every point is Osserman. We prove that a conformally Osserman manifold of dimension n 6= 3, 4, 16 is locally conformally equivalent either to a Euclidean space or to a...

A quaternionic calculus for surface pairs in the conformal 4-sphere is elaborated. This calculus is then used to discuss the relation between curved flats in the symmetric space of point pairs and Darboux and Christoffel pairs of isothermic surfaces. A new viewpoint on relations between surfaces of constant mean curvature in certain space forms is presented — in particular, a new form of Bryant...

We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a symmetry breaking when an asymmetric stationary state becomes energetically more favorable than a symmetric stationary state. We show that the energy of localized states decreases with increasing curvature, i.e., bending is a trap for nonlinear excitations. A violation of the...

The main purpose of this article is to provide an alternate proof to a result of Perelman on gradient shrinking solitons. Moreover in dimension three our proof generalizes Perelman’s result by removing the κ-non-collapsing assumption and allowing general curvature growth. The method also allows us to prove a classification result on gradient shrinking solitons with vanishing Weyl curvature tens...