8274

7672

كارشناسي ارشد

رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده رياضي

1392

نه، 83ص: مصور، جدول، نمودار

ص.ع:به فارسي و انگليسي

رياضي

ID7672

به فارسي و انگليسي: قابل رويت در نسخه ديجيتال

Homogeneous Lorentzian manifolds of a semisimple group Meysam Oshall m oshall@math iut ac ir 19 09 2012 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr M Aghasi m aghasi@cc iut ac ir Advisor Dr A Etemad Dehkordy ae110mat @cc iut ac ir 2010 MSC 53C75 22E46 Keywords Invariant metrics Lorentzian metrics Homogeneous manifolds AbstractA homogeneous manifold is a manifold together with a transitive action of a Lie group G on M Transitivity means that for any x y M there exists g G such that gx y In other words G hasonly one orbit on M A homogeneous manifold M may be identi ed with the coset space G K whereK g G go g is the stabilizer or stability subgroup of a point o M By a homogeneous manifold M G H we will understand the homogeneous manifold of a connectedLie group G modulo a closed connected subgroup H We identify the tangent space ToM at the pointo eH with the coset space V g h where g Lie G is the Lie algebra of G and h Lie H is thesubalgebra associated with the subgroup H We denote by j H GL V resp j h gl V theisotropy representation of the stability subgroup H resp the stability subalgebra h It is inducedby the adjoint representation of H resp h Since the group H is connected a tensor T in V isj H invariant if and only if it is j h invariant that is j h T 0 for all h h We describe the structure of d dimensional homogeneous Lorentzian G manifolds of the form M G H of a semisimple Lie group G Due to a result by N Kowalsky it is su cient to consider the casewhen the group G acts properly that is the stabilizer H is compact Then any homogeneous space with a smaller group H H admits an invariant Lorentzian metric A homogeneous manifold G HG H with a connected compact stabilizer H is called a minimal admissible manifold if it admits an Ginvariant Lorentzian metric but no homogeneous G manifold with a larger connected compact H

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