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TitleMathematical Physics, Analysis and Geometry - Volume 11
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LanguageEnglish
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Total Pages392
Table of Contents
                            On the Flag Curvature of Invariant Randers Metrics
	On the Flag Curvature of Invariant Randers Metrics
		Abstract
			Introduction
			Flag Curvature of Invariant Randers Metrics on Homogeneous Spaces
			Invariant Randers Metrics on Lie Groups
			References
Block Toeplitz Determinants, Constrained KP and Gelfand-Dickey Hierarchies
	Abstract
Degree Complexity of a Family of Birational Maps
	Abstract
Phase Vortex: A Dynamical System Approach
	Abstract
Algebraic Theory of Linear Viscoelastic Nematodynamics
A Wegner-type Estimate for Correlated Potentials
	Abstract
		Introduction
		Stollmann's Lemma for Product Measures
		Extension to Multi-particle Systems
		Extension to Correlated Random Variables
		Application to Gibbs Fields with Continuous Spin
		Conclusion
		References
The Two-Spectra Inverse Problem for Semi-infinite Jacobi Matrices in The Limit-Circle Case
	Abstract
Anisotropic Lavine™s Formula and Symmetrised Time Delay in Scattering Theory
	Abstract
Estimates for Entries of Matrix Valued Functions of Infinite Matrices
	Abstract
Rational Functions with a General Distribution of Poles on the Real Line Orthogonal with Respect to Varying Exponential Weights: I
	Abstract
Spectrum of the Lichnerowicz Laplacian on Asymptotically Hyperbolic Surfaces
	Abstract
		Introduction
		Definitions, Notations and Conventions
		Commutators of Some Natural Operators
		Some Decompositions of Trace Free Symmetric Two Tensors
		The Spectrum on TT-tensors
		Spectrum on Im L
		Conclusion
		Appendix : A Family of Cutoff Functions
		References
Some Examples of Graded C *-Algebras
	Abstract
                        
Document Text Contents
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Math Phys Anal Geom (2008) 11:1–9
DOI 10.1007/s11040-008-9037-8

On the Flag Curvature of Invariant Randers Metrics

Hamid Reza Salimi Moghaddam

Received: 10 December 2007 / Accepted: 6 February 2008 /
Published online: 21 March 2008
© Springer Science + Business Media B.V. 2008

Abstract In the present paper, the flag curvature of invariant Randers metrics
on homogeneous spaces and Lie groups is studied. We first give an explicit
formula for the flag curvature of invariant Randers metrics arising from
invariant Riemannian metrics on homogeneous spaces and, in special case, Lie
groups. We then study Randers metrics of constant positive flag curvature and
complete underlying Riemannian metric on Lie groups. Finally we give some
properties of those Lie groups which admit a left invariant non-Riemannian
Randers metric of Berwald type arising from a left invariant Riemannian
metric and a left invariant vector field.

Keywords Invariant metric · Flag curvature · Randers space ·
Homogeneous space · Lie group

Mathematics Subject Classifications (2000) 22E60 · 53C60 · 53C30

1 Introduction

The geometry of invariant structures on homogeneous spaces is one of the
interesting subjects in differential geometry. Invariant metrics are of these
invariant structures. K. Nomizu studied many interesting properties of in-
variant Riemannian metrics and the existence and properties of invariant
affine connections on reductive homogeneous spaces (see [14, 16]). Also some

H. R. S. Moghaddam (B)
Department of Mathematics, Shahrood University of Technology, Shahrood, Iran
e-mail: [email protected]

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