کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4606588 1337714 2010 5 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Gallot–Tanno theorem for pseudo-Riemannian metrics and a proof that decomposable cones over closed complete pseudo-Riemannian manifolds do not exist
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Gallot–Tanno theorem for pseudo-Riemannian metrics and a proof that decomposable cones over closed complete pseudo-Riemannian manifolds do not exist
چکیده انگلیسی

We generalize for complete pseudo-Riemannian metrics a classical result of Gallot (1979) [3] and Tanno (1978) [13]: we show that if a closed complete manifold admits a nonconstant function λ   satisfying ∇k∇j∇iλ+2∇kλ⋅gij+∇iλ⋅gjk+∇jλ⋅gik=0∇k∇j∇iλ+2∇kλ⋅gij+∇iλ⋅gjk+∇jλ⋅gik=0, then the metric is the Riemannian metric of constant curvature +1. We use this result to give a simple proof of a recent result of Alekseevsky, Cortes, Galaev and Leistner (2009) [1]. Certain generalizations for higher Gallot equations are given.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Differential Geometry and its Applications - Volume 28, Issue 2, April 2010, Pages 236–240
نویسندگان
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