کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4606583 1337714 2010 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A local classification of a class of (α,β)(α,β) metrics with constant flag curvature
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
A local classification of a class of (α,β)(α,β) metrics with constant flag curvature
چکیده انگلیسی

We first compute Riemannian curvature and Ricci curvature of (α,β)(α,β) metrics. Then we apply these formulae to discuss a special class (α,β)(α,β) metrics F=α(1+βα)p (|p|⩾1|p|⩾1) which have constant flag curvature. We obtain the sufficient and necessary conditions that F=(α+β)2α have constant flag curvature. Then we prove that such metrics must be locally projectively flat and complete their local classification. Using the same method we find a necessary condition that flag curvature of F=α2α+β is constant and proved that there are no non-trivial Matsumoto metrics. Furthermore, we give a negative answer whether there are non-trivial metrics F=α(1+βα)p (|p|⩾1|p|⩾1) of constant flag curvature when β is closed.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Differential Geometry and its Applications - Volume 28, Issue 2, April 2010, Pages 170–193
نویسندگان
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