نتایج جستجو برای: ricci parallel tensor

تعداد نتایج: 270534  

1995
M. Farhoudi

We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts (the Ricci tensor and the term proportional to the curvature scalar) with the trace relation between them is a common feature of any other homogeneous terms in the Lovelock tensor. Motivated by the principle of general invariance, we find that this property can be generalized, wit...

Journal: :Nonlinear Analysis-theory Methods & Applications 2021

In a Riemannian manifold with smooth positive function that weights the associated Hausdorff measures we study stable sets, i.e., second order minima of weighted perimeter under variations preserving volume. By assuming local convexity boundary and certain behavior Bakry–Émery–Ricci tensor deduce rigidity properties for sets by using deformations constructed from parallel vector fields tangent ...

Journal: :Journal of Nonlinear Mathematical Physics 2022

Abstract In this article, we investigate perfect fluid spacetimes equipped with concircular vector field. At first, in a spacetime admitting field, prove that the velocity field annihilates conformal curvature tensor. addition, dimension 4, show is generalized Robertson–Walker Einstein fibre. It proved if furnished admits second order symmetric parallel tensor P , then either equation of state ...

2012
Yann Ollivier YANN OLLIVIER

We try to provide a visual introduction to some objects used in Riemannian geometry: parallel transport, sectional curvature, Ricci curvature, Bianchi identities... We then explain some of the strategies used to define analogues of curvature in non-smooth or discrete spaces, beginning with Alexandrov curvature and δ-hyperbolic spaces, and insisting on various notions of generalized Ricci curvat...

2008
VESTISLAV APOSTOLOV

It is proved that a compact Kähler manifold whose Ricci tensor has two distinct constant non-negative eigenvalues is locally the product of two Kähler-Einstein manifolds. A stronger result is established for the case of Kähler surfaces. Irreducible Kähler manifolds with two distinct constant eigenvalues of the Ricci tensor are shown to exist in various situations: there are homogeneous examples...

1998
A. DIMAKIS

Within a framework of noncommutative geometry, we develop an analogue of (pseudo) Riemannian geometry on nite and discrete sets. On a nite set, there is a counterpart of the continuum metric tensor with a simple geometric interpretation. The latter is based on a correspondence between rst order di erential calculi and digraphs (the vertices of the latter are given by the elements of the nite se...

2009
Reto Müller

We consider a closed manifold M with a Riemannian metric gij(t) evolving by ∂t gij = −2Sij where Sij(t) is a symmetric two-tensor on (M, g(t)). We prove that if Sij satisfies the tensor inequality D(Sij , X) ≥ 0 for all vector fields X on M , where D(Sij , X) is defined in (1.6), then one can construct a forwards and a backwards reduced volume quantity, the former being non-increasing, the latt...

2003
ANNA FINO

The aim of this paper is to determine left-invariant strictly almost Kähler structures on 4-dimensional Lie groups (g, J,Ω) such that the Ricci tensor is J-invariant.

2007
Ion V. Vancea

We use the recent discovered x−ψ duality to parameterize spacetime in terms of wave functions and quantum prepotentials. The components of metric, connection, curvature, Ricci tensor and scalar curvature as well as Einstein equations in this parameterization are

2016
K L Duggal

We establish a link between a connection symmetry, called conformal collineation, and almost Ricci soliton (in particular Ricci soliton) in reducible Ricci symmetric semi-Riemannian manifolds. As a physical application, by investigating the kinematic and dynamic properties of almost Ricci soliton manifolds, we present a physical model of imperfect fluid spacetimes. This model gives a general re...

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