پديد آورنده :
ناصحي نجف آبادي، مهري
عنوان :
خواص هندسي فضاهاي همگن
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
منصور آقاسي
استاد مشاور :
اعظم اعتماد
توصيفگر ها :
گروه هاي لي حل پذير , منيفلدهاي همگن , ژئودزي هاي همگن , ساختارهاي اتصالي و مختلط پاياي چپ , سوليتن ريچي پاياي چپ , ساختارهاي همگن , مترهاي رندرز پاياي چپ
تاريخ نمايه سازي :
3/12/93
استاد داور :
اسداله رضوي، بهروز بيدآباد، فريد بهرامي
كد ايرانداك :
ID719 دكتري
چكيده انگليسي :
On Geometrical Properties of Homogeneous Spaces Mehri Nasehi Najafabadi m nasehi@math iut ac ir Jan 20 2015 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mansour Aghasi m aghasi@cc iut ac ir Advisor Dr Azam Etemad ae110mat@cc iut ac ir Department Graduate Program Coordinator Dr Farid Bahrami fbahrami@cc iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Abstract In this thesis we investigate some geometrical properties of a class of solvable Lie groups M 2n 1 in both Riemannian and Lorentzian cases We also equip these spaces with a Ran ders metric F of Douglas type and study some of their geometrical properties in this case Furthermore we introduce and classify a geometrical structure on Lie groups which admit a left invariant Randers metric of Berwald type We also obtain all these structures on three dimensional Lie groups Moreover we improve a result for naturally reductive homogeneous Randers spaces and extend some results for a family of homogeneous spaces with a Randers metric F of Douglas type Keywords Left invariant Ricci solitons Harmonicity of invariant vector elds Invariant contact structures Homogeneous structures Mathematics Subject Classi cation 2010 53C30 53C22 53C15 1 Introduction The study of geometrical properties of homogeneous spaces is an interesting subject in dif ferential geometry Some of these properties are homogeneous geodesics homogeneous struc tures left invariant Ricci solitons invariant contact and complex structures which have many important applications in physics and mechanics For example homogeneous geodesics cor respond to relative equilibria in the classical problem of the motions of an asymmetrical rigid body in a gravitational eld 3 This enables us to reduce many classical mechanics motion equations to a geodesic equation in an appropriate manifold Also the study of the equation of motion of charged particles in 4 on di erent homogeneous spaces shows that such equa tions are generalization of homogeneous geodesic equations We rst started our study with a class of solvable Lie groups In fact for any integer n 1 1
استاد راهنما :
منصور آقاسي
استاد مشاور :
اعظم اعتماد
استاد داور :
اسداله رضوي، بهروز بيدآباد، فريد بهرامي
