کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1895124 1044281 2008 46 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Spectral analysis and geometry of a sub-Riemannian structure on S3S3 and S7S7
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
پیش نمایش صفحه اول مقاله
Spectral analysis and geometry of a sub-Riemannian structure on S3S3 and S7S7
چکیده انگلیسی

The purpose of this paper is to study the spectral properties of a sub-Laplacian on S3S3, i.e., we discuss the analytic continuation of its spectral zeta function, give explicit expressions of the residues and especially, we provide an expression of the zeta-regularized determinant of the sub-Laplacian   on S3S3. Also, we describe sub-Riemannian curves on S3S3 based on the Hopf bundle structure, together with a proof of Chow’s theorem for this case in a strong sense (= connecting property by globally smooth curves). A characterization of sub-Riemannian geodesics on S3S3 via an isoperimetric problem through the Hopf bundle is explained. Incidentally, we introduce a hypo-elliptic operator on P1CP1C descended from the sub-Laplacian on S3S3, which we call a spherical Grushin operator  . We determine the subspace where it degenerates and give an expression of the trace of its heat kernel by making use of the trace of the heat kernel of the sub-Laplacian. In case of S7S7, we limit ourselves to present the spectral zeta function of a sub-Laplacian.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 58, Issue 12, December 2008, Pages 1693–1738
نویسندگان
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