کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1894303 1044159 2009 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
پیش نمایش صفحه اول مقاله
Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta
چکیده انگلیسی

We discuss pseudo-Riemannian metrics on 2-dimensional manifolds such that the geodesic flow admits a nontrivial integral quadratic in velocities. We construct local normal forms of such metrics. We show that these metrics have certain useful properties similar to those of Riemannian Liouville metrics, namely:
• they admit geodesically equivalent metrics;
• one can use them to construct a large family of natural systems admitting integrals quadratic in momenta;
• the integrability of such systems can be generalized to the quantum setting;
• these natural systems are integrable by quadratures.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 59, Issue 7, July 2009, Pages 1048–1062
نویسندگان
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