کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5775132 1413576 2017 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the relation between Ricci-Harmonic solitons and Ricci solitons
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
On the relation between Ricci-Harmonic solitons and Ricci solitons
چکیده انگلیسی
Let (Mm,gij) and (Nn,hβγ) be two Riemannian manifolds, and ϕ:M→N a smooth map. By definition, a gradient Ricci-Harmonic soliton satisfies(0.1){Rij−α∇iϕ∇jϕ+∇i∇jf=λgij;τgϕ=∇iϕ∇if, for some f∈C∞(M) and constants α and λ. Here τgϕ=trg(∇dϕ) is the tension filed of ϕ. We prove that when α>0 and the sectional curvature of N is bounded from above by αm, any shrinking or steady Ricci-Harmonic soliton (i.e., λ>0 or λ=0, respectively) must be a Ricci soliton, namely, ϕ is a constant map. In particular, it implies that the shrinking and steady solitons generated from Bernhard List's flow [9] are exactly the corresponding solitons of the Ricci flow, and hence some recent results regarding the shrinking solitons of List's flow are actually duplications of the previous results for Ricci solitons.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 447, Issue 2, 15 March 2017, Pages 882-889
نویسندگان
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