پديد آورنده :
عضنفري، سعيد
عنوان :
مترانيشتن روي گروه هاي لي فشرده و همگن
مقطع تحصيلي :
كارشناسي ارشد
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 :
فضاهاي همگن , مترهاي كاهش يافته طبيعي , خمينه هاي فلگ , تاربندي
تاريخ نمايه سازي :
15/10/92
استاد داور :
فريد بهرامي، اسداله رضوي
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Einstein Metrics on Compact and Homogeneous Lie Groups Saeid Ghazanfari s ghazanfari@math iut ac ir 2013 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 2010 MSC 53C25 53C30 17B20 53C20 Keywords Einstein metrics Homogeneous spaces Naturally reductive metrics Kahler C Spaces Fibraton AbstractA Riemannian metric g is said to be Einstein if its Ricci curvature satis es the Einstein equationRic g g for some constant This system of equations is a complicated system of non linearsecond order partial di erential equations and at the present time no general existence results forEinstein metrics are known However there are results for many interesting classes of Einstein metrics such as compct andhomogeneous Einstein metrics Finding Einstein metrics on compact and homogeneous spaces is asubject of considerable mathematical interest It is also of importance in physics most notably insupergravity string theory or M theory backgrounds Motivated by this we study the question of the Gexistence of Einstein metrics on compact homogeneous spaces H both for the case where H is someproper subgroup of G and also for the case that H is the identity in which case the space is just thegroup manifold G itself If the Riemannian manifold M g is compact then an old result of Hilbert states that g is anEinstein metric if and only if g is a critical point of the scalar curvature functional This suggests avariational approach to nding Einstein metrics which in the homogeneous case has lead to severalimportant existence and non existence results mainly from the works of M Wang and W Ziller Also C B hm and M Kerr showed that every compact simply connected homogeneous space up todimension 11 admits at least one invariant Einstein metric It is known that in dimension 12 there are
استاد راهنما :
منصور آقاسي
استاد مشاور :
اعظم اعتماد
استاد داور :
فريد بهرامي، اسداله رضوي
