scholarly journals Nonlocal symmetry of CMA generates ASD Ricci-flat metric with no Killing vectors

2021 ◽  
Vol 62 (1) ◽  
pp. 013504
Author(s):  
M. B. Sheftel
Keyword(s):  
Nonlocal Symmetry ◽  
Killing Vectors ◽  
Ricci Flat ◽  
Flat Metric

scholarly journals A Ricci-flat metric on D-brane orbifolds

1998 ◽  
Vol 433 (3-4) ◽  
pp. 307-317 ◽  
Author(s):  
Koushik Ray
Keyword(s):  
Ricci Flat ◽  
Flat Metric

scholarly journals Existence of complete Kähler Ricci-flat metrics on crepant resolutions

2014 ◽  
Vol 16 (03) ◽  
pp. 1450003 ◽  
Author(s):  
Bianca Santoro
Keyword(s):  
Asymptotic Behavior ◽  
Existence Results ◽  
Kähler Metrics ◽  
Asymptotically Flat ◽  
Kahler Metrics ◽  
Ricci Flat ◽  
Crepant Resolutions ◽  
Flat Metric

In this note, we obtain existence results for complete Ricci-flat Kähler metrics on crepant resolutions of singularities of Calabi–Yau varieties. Furthermore, for certain asymptotically flat Calabi–Yau varieties, we show that the Ricci-flat metric on the resolved manifold has the same asymptotic behavior as the initial variety.

scholarly journals Weighted projective Ricci curvature in Finsler geometry

2021 ◽  
Vol 71 (1) ◽  
pp. 183-198
Author(s):  
Tayebeh Tabatabaeifar ◽  
Behzad Najafi ◽  
Akbar Tayebi
Keyword(s):  
Ricci Curvature ◽  
Finsler Geometry ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Randers Metric ◽  
Ricci Flat ◽  
Projectively Flat ◽  
Flat Metric ◽  
Necessary And Sufficient ◽  
Randers Metrics

Abstract In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric with isotropic weighted projective Ricci and isotropic S-curvature is a Kropina metric or Randers metric.

scholarly journals A new incomplete Ricci-flat metric

2019 ◽  
Vol 16 (05) ◽  
pp. 1950077
Author(s):  
E. G. Malkovich
Keyword(s):  
Singular Point ◽  
Explicit Formula ◽  
Riemannian Metric ◽  
Ricci Flat ◽  
Flat Metric

Classical metrics (Eguchi–Hanson, Taub–NUT, Fubini–Study) satisfy a certain system of ODE that we introduced. By studying this system we found new Ricci-flat incomplete Riemannian metric in explicit formula and described its behavior at infinity and in the singular point.

scholarly journals Resolution à la Kronheimer of $$\mathbb {C}^3/\Gamma $$ singularities and the Monge–Ampère equation for Ricci-flat Kähler metrics in view of D3-brane solutions of supergravity

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Massimo Bianchi ◽  
Ugo Bruzzo ◽  
Pietro Fré ◽  
Dario Martelli
Keyword(s):  
Exceptional Divisor ◽  
The Other ◽  
Canonical Bundle ◽  
Kähler Metrics ◽  
Kähler Metric ◽  
Kahler Metrics ◽  
Ricci Flat ◽  
Flat Metric ◽  
Kahler Metric ◽  
Monge Ampere

AbstractIn this paper, we analyze the relevance of the generalized Kronheimer construction for the gauge/gravity correspondence. We begin with the general structure of D3-brane solutions of type IIB supergravity on smooth manifolds $$Y^\Gamma $$ Y Γ that are supposed to be the crepant resolution of quotient singularities $$\mathbb {C}^3/\Gamma $$ C 3 / Γ with $$\Gamma $$ Γ a finite subgroup of SU(3). We emphasize that nontrivial 3-form fluxes require the existence of imaginary self-dual harmonic forms $$\omega ^{2,1}$$ ω 2 , 1 . Although excluded in the classical Kronheimer construction, they may be reintroduced by means of mass deformations. Next we concentrate on the other essential item for the D3-brane construction, namely, the existence of a Ricci-flat metric on $$Y^\Gamma $$ Y Γ . We study the issue of Ricci-flat Kähler metrics on such resolutions $$Y^\Gamma $$ Y Γ , with particular attention to the case $$\Gamma =\mathbb {Z}_4$$ Γ = Z 4 . We advance the conjecture that on the exceptional divisor of $$Y^\Gamma $$ Y Γ the Kronheimer Kähler metric and the Ricci-flat one, that is locally flat at infinity, coincide. The conjecture is shown to be true in the case of the Ricci-flat metric on $$\mathrm{tot} K_{{\mathbb {W}P}[112]}$$ tot K W P [ 112 ] that we construct, i.e., the total space of the canonical bundle of the weighted projective space $${\mathbb {W}P}[112]$$ W P [ 112 ] , which is a partial resolution of $$\mathbb {C}^3/\mathbb {Z}_4$$ C 3 / Z 4 . For the full resolution, we have $$Y^{\mathbb {Z}_4}={\text {tot}} K_{\mathbb {F}_{2}}$$ Y Z 4 = tot K F 2 , where $$\mathbb {F}_2$$ F 2 is the second Hirzebruch surface. We try to extend the proof of the conjecture to this case using the one-parameter Kähler metric on $$\mathbb {F}_2$$ F 2 produced by the Kronheimer construction as initial datum in a Monge–Ampère (MA) equation. We exhibit three formulations of this MA equation, one in terms of the Kähler potential, the other two in terms of the symplectic potential but with two different choices of the variables. In both cases, one can establish a series solution in powers of the variable along the fibers of the canonical bundle. The main property of the MA equation is that it does not impose any condition on the initial geometry of the exceptional divisor, rather it uniquely determines all the subsequent terms as local functionals of this initial datum. Although a formal proof is still missing, numerical and analytical results support the conjecture. As a by-product of our investigation, we have identified some new properties of this type of MA equations that we believe to be so far unknown.

ON A PERFECT FLUID K¨ AHLER SPACETIME

2016 ◽  
Vol 12 (3) ◽  
pp. 4350-4355
Author(s):  
VIBHA SRIVASTAVA ◽  
P. N. PANDEY
Keyword(s):  
Field Equation ◽  
Perfect Fluid ◽  
Sectional Curvature ◽  
Einstein Field Equation ◽  
Cosmological Term ◽  
Conformal Killing ◽  
Killing Vectors ◽  
Projectively Flat ◽  
Conformal Killing Vectors

The object of the present paper is to study a perfect fluid K¨ahlerspacetime. A perfect fluid K¨ahler spacetime satisfying the Einstein field equation with a cosmological term has been studied and the existence of killingand conformal killing vectors have been discussed. Certain results related to sectional curvature for pseudo projectively flat perfect fluid K¨ahler spacetime have been obtained. Dust model for perfect fluid K¨ahler spacetime has also been studied.

Killing vectors in gauge supersymmetry

1978 ◽  
Vol 19 (10) ◽  
pp. 2203 ◽  
Author(s):  
L. Kannenberg
Keyword(s):  
Killing Vectors
Sign in / Sign up

Export Citation Format

Share Document