Scalar concomitants of a metric and a curvature form

1988 ◽  
Vol 20 (4) ◽  
pp. 337-342 ◽  
Author(s):  
R. J. Noriega ◽  
D. Pr�lat ◽  
C. G. Schifini
Keyword(s):  
Curvature Form

Vertical Chern Type Classes on Complex Finsler Bundles

2011 ◽  
Vol 57 (2) ◽  
pp. 377-386
Author(s):  
Cristian Ida
Keyword(s):  
Differential Forms ◽  
Linear Connection ◽  
Curvature Form ◽  
Cohomology Groups ◽  
Finsler Manifolds ◽  
Invariance Properties ◽  
Type Classes

Vertical Chern Type Classes on Complex Finsler BundlesIn the present paper, we define vertical Chern type classes on complex Finsler bundles, as an extension of thev-cohomology groups theory on complex Finsler manifolds. These classes are introduced in a classical way by using closed differential forms with respect to the conjugated vertical differential in terms of the vertical curvature form of Chern-Finsler linear connection. Also, some invariance properties of these classes are studied.

scholarly journals THE CONSERVED CHARGES AND INTEGRABILITY OF THE CONFORMAL AFFINE TODA MODELS

1994 ◽  
Vol 09 (30) ◽  
pp. 2783-2801 ◽  
Author(s):  
H. ARATYN ◽  
L. A. FERREIRA ◽  
J. F. GOMES ◽  
A. H. ZIMERMAN
Keyword(s):  
Poisson Bracket ◽  
Equations Of Motion ◽  
Curvature Form ◽  
Two Dimensional ◽  
Conserved Charges ◽  
Zero Curvature ◽  
Algebraic Properties ◽  
Toda Model ◽  
Infinite Sets ◽  
Poisson Commute

We construct infinite sets of local conserved charges for the conformal affine Toda model. The technique involves the abelianization of the two-dimensional gauge potentials satisfying the zero-curvature form of the equations of motion. We find two infinite sets of chiral charges and apart from two lowest spin charges, all the remaining ones do not possess chiral densities. Charges of different chiralities Poisson commute among themselves. We discuss the algebraic properties of these charges and use the fundamental Poisson bracket relation to show that the charges conserved in time are in involution. Connections to other Toda models are established by taking particular limits.

scholarly journals A Note on the Liouville Equation

1981 ◽  
Vol 36 (4) ◽  
pp. 417-418
Author(s):  
A. Grauel
Keyword(s):  
Lie Algebra ◽  
Liouville Equation ◽  
Curvature Form ◽  
Geometrical Features ◽  
Non Linear

We study some geometrical features of the non-linear scattering equations [1]. From this we deduce the Liouville equation. For that we interpret the SL(2, ℝ)-valued elements of the matrices in the scattering equations as matrix-valued forms and calculate the curvature 2-form with respect to a basis of the Lie algebra. We obtain the Liouville equation if the curvature form is equal to zero

scholarly journals Riemannian foliations and the kernel of the basic Dirac operator

2012 ◽  
Vol 20 (2) ◽  
pp. 145-158
Author(s):  
Vladimir Slesar
Keyword(s):  
Dirac Operator ◽  
Mean Curvature ◽  
Riemannian Foliation ◽  
Curvature Form ◽  
Harmonic Mean ◽  
Riemannian Foliations ◽  
Bochner Technique ◽  
The Mean ◽  
Traditional Setting ◽  
Rela Tions

Abstract In this paper, in the special setting of a Riemannian foliation en- dowed with a bundle-like metric, we obtain conditions that force the vanishing of the kernel of the basic Dirac operator associated to the metric; this way we extend the traditional setting of Riemannian foli- ations with basic-harmonic mean curvature, where Bochner technique and vanishing results are known to work. Beside classical conditions concerning the positivity of some curvature terms we obtain new rela- tions between the mean curvature form and the kernel of the basic Dirac operator

scholarly journals Mean value surfaces with prescribed curvature form

2004 ◽  
Vol 83 (9) ◽  
pp. 1075-1107 ◽  
Author(s):  
Håkan Hedenmalm ◽  
Yolanda Perdomo G
Keyword(s):  
Mean Value ◽  
Curvature Form ◽  
Prescribed Curvature

Scalar concomitants of a metric and a curvature form. II

1989 ◽  
Vol 30 (3) ◽  
pp. 617-618 ◽  
Author(s):  
R. J. Noriega ◽  
C. G. Schifini
Keyword(s):  
Curvature Form

scholarly journals Remarks on Kähler-Einstein Manifolds

1972 ◽  
Vol 46 ◽  
pp. 161-173 ◽  
Author(s):  
Yozo Matsushima
Keyword(s):  
Einstein Metrics ◽  
Integral Formula ◽  
Curvature Form ◽  
Einstein Metric ◽  
Kähler Metric ◽  
Kähler Einstein Metrics ◽  
Simply Connected ◽  
Kahler Metric ◽  
Complex Projective ◽  
Ricci Form

The main purpose of this note is to characterize a compact Káhler-Einstein manifold in terms of curvature form. The curvature form Q is an EndT valued differential form of type (1,1) which represents the curvature class of the manifold. We shall prove that the curvature form of a Káhler metric is the harmonic representative of the curvature class if and only if the Káhler metric is an Einstein metric in the generalized sense (g.s.), that is, if the Ricci form of the metric is parallel. It is well known that a Káhler metric is an Einstein metric in the g. s. if and only if it is locally product (globally, if the manifold is simply connected and complete) of Kàhler-Einstein metrics. We obtain an integral formula, involving the integral of the trace of some operators defined by the curvature tensor, which measures the deviation of a Káhler-Einstein metric from a Hermitian symmetric metric. In the final section we shall prove the uniqueness up to equivalence of Kãhler-Einstein metrics in a simply connected compact complex homogeneous space. This result was proved by Berger in the case of a complex projective space and our proof is completely different from Berger’s.

scholarly journals Convergence results for two Kähler–Ricci flows

2014 ◽  
Vol 25 (09) ◽  
pp. 1450084
Author(s):  
Zhou Zhang
Keyword(s):  
Ricci Curvature ◽  
Einstein Metrics ◽  
Curvature Form ◽  
Volume Form ◽  
Ricci Flows ◽  
Convergence Results ◽  
Smooth Convergence ◽  
Kähler Einstein Metrics

In this note, we provide some general discussion on the two main versions in the study of Kähler–Ricci flows over closed manifolds, aiming at smooth convergence to the corresponding Kähler–Einstein metrics with assumptions on the volume form and Ricci curvature form along the flow.

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