Related papers: 2-Riemannian manifolds

A semi-Riemannian metric in a n-manifold has n(n-1)/2 degrees of freedom, i.e. as many as the number of components of a differential 2-form. We prove that any semi-Riemannian metric can be obtained as a deformation of a constant curvature…

On the product of two Finsler manifolds M1 M2, we consider the twisted metric F which is construct by using Finsler metrics F1 and F2 on the manifolds M1 and M2, respectively. We introduce horizontal and vertical distributions on twisted…

Suppose that there exists a discrete subset $X$ of a complete, connected, $n$-dimensional Riemannian manifold $M$ such that the Riemannian distances between points of $X$ correspond to the Euclidean distances of a net in $\mathbb{R}^{n}$.…

We obtained that any 2-form and any smooth function on 2-manifolds with boundary can be realized as the curvature form and the gaussian curvature function of some Riemmanian metric, respectively.

We give necessary and sufficient conditions for a semi-Riemannian manifold of arbitrary signature to be locally isometrically immersed into certain warped products. Then, we describe a way to use the structure equations of such immersions…

We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a…

In this paper we extend the Cartan's approach of Riemannian normal coordinates and show that all n-dimensional pseudo-Riemannian metrics are conformal to a flat manifold, when, in normal coordinates, they are well-behaved in the origin and…

In Riemann geometry, the relations among two transversal submanifolds and global manifold are discussed. By replacing the normal vector of a submanifold with the tangent vector of another submanifold, the metric tensors, Christoffel symbols…

A pseudo-Riemannian manifold endowed with $k>2$ orthogonal complementary distributions (called a Riemannian almost multi-product structure) appears in such topics as multiply warped products, the webs composed of several foliations, Dupin…

The space of all non degenerate bilinear structures on a manifold $M$ carries a one parameter family of pseudo Riemannian metrics. We determine the geodesic equation, covariant derivative, curvature, and we solve the geodesic equation…

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute the connection forms of these metrics and the higher symbols of their curvature forms,…

A totally umbilical submanifold in pseudo-Riemannian manifolds is a fundamental notion, which is characterized by the condition that the second fundamental form is proportional to the metric. It is also a generalization of the notion of a…

For the Riemannian manifold $M^{n}$ two special connections on the sum of the tangent bundle $TM^{n}$ and the trivial one-dimensional bundle are constructed. These connections are flat if and only if the space $M^{n}$ has a constant…

In this study, the geometric properties of null helices on a totally umbilical submanifold within a three-dimensional semi-Riemannian manifold are investigated. The pseudo-Riemannian metric structure of semi-Riemannian manifolds and the…

In this paper, we have reintroduced a new approach to conformal geometry developed and presented in two previous papers, in which we show that all n-dimensional pseudo-Riemannian metrics are conformal to a flat n-dimensional manifold as…

For constant mean curvature surfaces of class $C^2$ immersed inside Sasakian sub-Riemannian 3-manifolds we obtain a formula for the second derivative of the area which involves horizontal analytical terms, the Webster scalar curvature of…

On Hermitian manifolds, the second Ricci curvature tensors of various metric connections are closely related to the geometry of Hermitian manifolds. By refining the Bochner formulas for any Hermitian complex vector bundle (Riemannain real…

We give coordinate formula and geometric description of the curvature of the tensor product connection of linear connections on vector bundles with the same base manifold. We define the covariant differential of geometric fields of certain…

The authors define a SNS (semi-nearly-sub)-Riemannian connection on nearly sub-Riemannian manifolds and study the geometric properties of such a connection, and obtain the natures of horizontal curvature tensors between horizontal…

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. Generically, there are…