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Yavari, Negar, ‎Alipour-Fakhri, Yousef. (1404). Geometry of warped tangent bundles with Ricci-Flatness and shrinking solitions. سامانه مدیریت نشریات علمی, (), 103-119. doi: 10.22098/jfga.2025.17749.1168
Negar Yavari; Yousef ‎Alipour-Fakhri. "Geometry of warped tangent bundles with Ricci-Flatness and shrinking solitions". سامانه مدیریت نشریات علمی, , , 1404, 103-119. doi: 10.22098/jfga.2025.17749.1168
Yavari, Negar, ‎Alipour-Fakhri, Yousef. (1404). 'Geometry of warped tangent bundles with Ricci-Flatness and shrinking solitions', سامانه مدیریت نشریات علمی, (), pp. 103-119. doi: 10.22098/jfga.2025.17749.1168
Yavari, Negar, ‎Alipour-Fakhri, Yousef. Geometry of warped tangent bundles with Ricci-Flatness and shrinking solitions. سامانه مدیریت نشریات علمی, 1404; (): 103-119. doi: 10.22098/jfga.2025.17749.1168

Geometry of warped tangent bundles with Ricci-Flatness and shrinking solitions

Journal of Finsler Geometry and its Applications
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 مرداد 1404    اصل مقاله (368.36 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2025.17749.1168
نویسندگان
Negar Yavari؛ Yousef ‎Alipour-Fakhri*
Department of Mathematics, Payame Noor University 19395-3697, Tehran, Iran
چکیده
‎In this paper‎, ‎we investigate the geometric structure of the tangent bundle of a warped product of two pseudo-Riemannian manifolds‎. ‎Let (M,g) and (M-,g-) be smooth pseudo-Riemannian manifolds‎, ‎and consider the‎‎warped product manifold (M×M-,g+e2fg-)‎, ‎where f is a smooth warping function‎. ‎We construct a Sasaki–Matsumoto type lift of the warped metric to define a pseudo-Riemannian metric on the tangent bundle‎, ‎which depends on a pair of smooth scalar functions and related to the total kinetic energy‎. We derive necessary and sufficient conditions under which the lifted metric on is Ricci-flat‎, ‎expressed in terms of the curvature properties of the base manifold and the structure functions‎. ‎Furthermore‎, ‎we prove that‎, ‎equipped with the metric‎, ‎admits a one-parameter family of shrinking Ricci solitons‎.
کلیدواژه‌ها
Ricci flat‎؛ ‎warped pseudo Riemannian manifold؛ Ricci soliton
مراجع
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2. B. Chow, et al, The Ricci Flow: Thechniques and Applications. Part I: Geometric Aspects, American Mathematical Socity, (2007).
3. R. Deszcz and M. Kucharski, On curvature properties of certain generalized RobertsonWalker spacetimes, Tsukuba J. Math. 23(1999) , 113-130.
4. J. Kern, Lagrange Geometry, Arch. Math. (Basel). 25(1974), 438-443.
5. G.I. Kruchkovich, On some class of Riemannian spaces(in Russian), Trudy sem. po vekt.i tenz. analizu 11(1961), 103-128.
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7. N. Papaghiuc, A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold, Colloq. Math. 87 (2) (2001), 227-233, MR 1814664 (2002a:53086). 

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