scholarly journals A Note on the Characterization of Two-Dimensional Quasi-Einstein Manifolds

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2013
Author(s):  
Gabriel Bercu
Keyword(s):  
Constant Curvature ◽  
Riemannian Manifolds ◽  
Warped Product ◽  
Product Type ◽  
Two Dimensional ◽  
Einstein Manifolds ◽  
Local Coordinates ◽  
Elementary Methods

In this article, we aim to introduce new classes of two-dimensional quasi-Einstein pseudo-Riemannian manifolds with constant curvature. We also give a classification of 2D quasi-Einstein manifolds of warped product type working in local coordinates. All the results are obtained by elementary methods.

Some curvature restricted geometric structures for projective curvature tensors

2018 ◽  
Vol 15 (09) ◽  
pp. 1850157 ◽  
Author(s):  
Absos Ali Shaikh ◽  
Haradhan Kundu
Keyword(s):  
Curvature Tensor ◽  
Riemannian Manifolds ◽  
Einstein Manifolds ◽  
Geometric Structures ◽  
Projective Curvature ◽  
Riemannian Case ◽  
Projective Curvature Tensor ◽  
Projective Operator ◽  
Curvature Tensors

The projective curvature tensor is an invariant under geodesic preserving transformations on semi-Riemannian manifolds. It possesses different geometric properties than other generalized curvature tensors. The main object of the present paper is to study some semisymmetric type and pseudosymmetric type curvature restricted geometric structures due to projective curvature tensor. The reduced pseudosymmetric type structures for various Walker type conditions are deduced and the existence of Venzi space is ensured. It is shown that the geometric structures formed by imposing projective operator on a (0,4)-tensor is different from that for the corresponding (1,3)-tensor. Characterization of various semisymmetric type and pseudosymmetric type curvature restricted geometric structures due to projective curvature tensor are obtained on semi-Riemannian manifolds, and it is shown that some of them reduce to Einstein manifolds for the Riemannian case. Finally, to support our theorems, four suitable examples are presented.

A NOTE ON THE CLASSIFICATION OF NONCOMPACT QUASI-EINSTEIN MANIFOLDS WITH VANISHING CONDITION ON THE WEYL TENSOR

2021 ◽  
pp. 1-11
Author(s):  
H. BALTAZAR ◽  
M. MATOS NETO
Keyword(s):  
Fourth Order ◽  
Weyl Tensor ◽  
Warped Product ◽  
Einstein Manifold ◽  
Dimensional Manifold ◽  
Einstein Manifolds ◽  
Weyl Curvature ◽  
Nonnegative Ricci Curvature ◽  
Simply Connected

Abstract The aim of this paper is to study complete (noncompact) m-quasi-Einstein manifolds with λ=0 satisfying a fourth-order vanishing condition on the Weyl tensor and zero radial Weyl curvature. In this case, we are able to prove that an m-quasi-Einstein manifold (m>1) with λ=0 on a simply connected n-dimensional manifold(M n , g), (n ≥ 4), of nonnegative Ricci curvature and zero radial Weyl curvature must be a warped product with (n–1)–dimensional Einstein fiber, provided that M has fourth-order divergence-free Weyl tensor (i.e. div4W =0).

CLASSIFICATION OF TYPES OF SOCIETAL CONFLICTS AND CHARACTERIZATION OF THEIR RESOLUTION PROCESSES BASED ON DEONTIC LOGIC

2002 ◽  
Vol 04 (03) ◽  
pp. 213-236 ◽  
Author(s):  
OSAMU KATAI ◽  
KENTARO TODA ◽  
HIROSHI KAWAKAMI
Keyword(s):  
General Theory ◽  
Deontic Logic ◽  
The Other ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
Normative Concepts ◽  
Resolution Processes ◽  
Type Classification

Focusing on the interaction among members' attitudes toward issues of common concern and members' expectance toward other members' attitudes, type classification of societal conflicts and their degree of strength are clarified. For the purpose, a vigorous theoretical framework for the examination of interrelationships among various normative concepts such as obligation, permission, prohibition, etc. is introduced, on the basis of the general theory on norms, deontic logic. By presuming several plausible laws on the way of the resolution of these conflicts and by introducing a two-dimensional representation of the conflicts with one axis representing the degree of imbalance and the other axis representing the cohesiveness of systems, a characterization method of conflict resolution processes is obtained, through which prediction and analysis of actual resolution processes can be done.

Riemannian manifolds whose curvature operator R(X, Y) has constant eigenvalues

2004 ◽  
Vol 70 (2) ◽  
pp. 301-319 ◽  
Author(s):  
Y. Nikolayevsky
Keyword(s):  
Riemannian Manifold ◽  
Constant Curvature ◽  
Riemannian Manifolds ◽  
Warped Product ◽  
Curvature Operator ◽  
Specific Function ◽  
3 Dimensional ◽  
Space Of Constant Curvature

A Riemannian manifold Mn is called IP, if, at every point x ∈ Mn, the eigenvalues of its skew-symmetric curvature operator R(X, Y) are the same, for every pair of orthonormal vectors X, Y ∈ TxMn. In [5, 6, 12] it was shown that for all n ≥ 4, except n = 7, an IP manifold either has constant curvature, or is a warped product, with some specific function, of an interval and a space of constant curvature. We prove that the same result is still valid in the last remaining case n = 7, and also study 3-dimensional IP manifolds.

scholarly journals Non-reductive Homogeneous Pseudo-Riemannian Manifolds of Dimension Four

2006 ◽  
Vol 58 (2) ◽  
pp. 282-311 ◽  
Author(s):  
M. E. Fels ◽  
A. G. Renner
Keyword(s):  
Riemannian Manifold ◽  
Constant Curvature ◽  
Riemannian Manifolds ◽  
Homogeneous Spaces ◽  
Isotropy Subgroup ◽  
Algebraic Classification ◽  
Ricci Flat ◽  
Einstein Spaces ◽  
Simply Connected

AbstractA method, due to Élie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2, 2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is simply connected, then it is shown to be diffeomorphic to ℝ4. All metrics for the simply connected non-reductive Einstein spaces are given explicitly. There are no non-reductive pseudo-Riemannian homogeneous spaces of dimension two and none of dimension three with connected isotropy subgroup.

Sign in / Sign up

Export Citation Format

Share Document