Application of the Weyl curvature tensor to description of the generalized Reissner-Nordstrøm space-time

2000 ◽  
Vol 27 (2) ◽  
pp. 219-223
Author(s):  
Barbara Glanc ◽  
Antoni Jakubowicz
Keyword(s):  
Curvature Tensor ◽  
Space Time ◽  
Weyl Curvature ◽  
Weyl Curvature Tensor

scholarly journals On a New type of Tensor on Real Hypersurfaces in Non-Flat Complex Space Forms

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 559
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou
Keyword(s):  
Curvature Tensor ◽  
Complex Space ◽  
Three Dimensional ◽  
Real Hypersurfaces ◽  
Weyl Curvature ◽  
Space Forms ◽  
Hopf Hypersurfaces ◽  
Weyl Curvature Tensor ◽  
New Type ◽  
Complex Space Forms

In this paper the notion of ∗ -Weyl curvature tensor on real hypersurfaces in non-flat complex space forms is introduced. It is related to the ∗ -Ricci tensor of a real hypersurface. The aim of this paper is to provide two classification theorems concerning real hypersurfaces in non-flat complex space forms in terms of ∗ -Weyl curvature tensor. More precisely, Hopf hypersurfaces of dimension greater or equal to three in non-flat complex space forms with vanishing ∗ -Weyl curvature tensor are classified. Next, all three dimensional real hypersurfaces in non-flat complex space forms, whose ∗ -Weyl curvature tensor vanishes identically are classified. The used methods are based on tools from differential geometry and solving systems of differential equations.

scholarly journals CURVATURE STRUCTURE OF SELF-DUAL 4-MANIFOLDS

2008 ◽  
Vol 05 (07) ◽  
pp. 1191-1204 ◽  
Author(s):  
NOVICA BLAŽIĆ ◽  
PETER GILKEY ◽  
STANA NIKČEVIĆ ◽  
IVA STAVROV
Keyword(s):  
Curvature Tensor ◽  
Riemannian Manifolds ◽  
Weyl Curvature ◽  
Weyl Curvature Tensor ◽  
Algebraic Result ◽  
Curvature Structure

We show the existence of a modified Cliff(1,1)-structure compatible with an Osserman 0-model of signature (2,2). We then apply this algebraic result to certain classes of pseudo-Riemannian manifolds of signature (2,2). We obtain a new characterization of the Weyl curvature tensor of an (anti-)self-dual manifold and we prove some new results regarding (Jordan) Osserman manifolds.

scholarly journals *-Weyl Curvature Tensor within the Framework of Sasakian and $(\kappa,\mu)$-Contact Manifolds

2021 ◽  
Vol 52 ◽  
Author(s):  
Venkatesha Venkatesha ◽  
H. Aruna Kumara
Keyword(s):  
Curvature Tensor ◽  
Contact Manifolds ◽  
Weyl Curvature ◽  
Weyl Curvature Tensor

The object of the present paper is to study $*$-Weyl curvature tensor within the framework of Sasakian and $(\kappa,\mu)$-contact manifolds.

scholarly journals On isospectral compactness in conformal class for 4-manifolds

2019 ◽  
Vol 21 (05) ◽  
pp. 1850041 ◽  
Author(s):  
Xianfu Liu ◽  
Zuoqin Wang
Keyword(s):  
Scalar Curvature ◽  
Curvature Tensor ◽  
Riemannian Metrics ◽  
Conformal Class ◽  
Weyl Curvature ◽  
Yamabe Invariant ◽  
Weyl Curvature Tensor

Let [Formula: see text] be a closed 4-manifold with positive Yamabe invariant and with [Formula: see text]-small Weyl curvature tensor. Let [Formula: see text] be any metric in the conformal class of [Formula: see text] whose scalar curvature is [Formula: see text]-close to a constant. We prove that the set of Riemannian metrics in the conformal class [Formula: see text] that are isospectral to [Formula: see text] is compact in the [Formula: see text] topology.

scholarly journals The Weyl Curvature Tensor of Hypersurfaces Under the Mean Curvature Flow

2020 ◽  
Vol 76 (1) ◽  
pp. 143-156
Author(s):  
Ghodrat Moazzaf ◽  
Esmaiel Abedi
Keyword(s):  
Curvature Tensor ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Conformally Flat ◽  
Weyl Curvature ◽  
Initial Hypersurface ◽  
Weyl Curvature Tensor ◽  
The Mean ◽  
Upper Estimate

AbstractIn this paper, we study the evolution of the Weyl curvature tensor W of hypersurfaces in 𝕉n+1 under the mean curvature flow. We find a bound for the Weyl curvature tensor of hypersurfaces during the evolution in terms of time. As a consequence, we suppose that the initial hypersurface is conformally flat, i.e., W =0 at t = 0 and then we find an upper estimate for W during the evolution in terms of time.

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