مشخصات پژوهش

عنوان	ON TIMELIKE HYPERSURFACES OF THE MINKOWSKI 4-SPACE WITH 1-PROPER SECOND MEAN CURVATURE VECTOR
نوع پژوهش	مقاله چاپ‌شده در مجلات علمی
کلیدواژه‌ها	Weak convex, Lorentz hypersurface, Biharmonic, C-harmonic
چکیده	The mean curvature vector field of a submanifold in the Eu- clidean n-space is said to be proper if it is an eigenvector of the Laplace operator ∆. It is proven that every hypersurface with proper mean cur- vature vector field in the Euclidean 4-space E4 has constant mean cur- vature. In this paper, we study an extended version of the mentioned subject on timelike (i.e., Lorentz) hypersurfaces of Minkowski 4-space E4 1. Let x : M 3 1 → E4 1 be the isometric immersion of a timelike hyper- surface M 3 1 in E4 1. The second mean curvature vector field H2 of M 3 1 is called 1-proper if it is an eigenvector of the Cheng-Yau operator C (which is the natural extension of ∆). We show that each M 3 1 with 1-proper H2 has constant scalar curvature. By a classification theorem, we show that such a hypersurface is C-biharmonic, C-1-type or null-C-2-type. Since the shape operator of M 3 1 has four possible matrix forms, the results will be considered in four different cases.
پژوهشگران	لیلا شهباز (نفر چهارم)، اصغر رحیمی (نفر سوم)، ناصر تنومند خوشه مهر (نفر دوم)، فیروز پاشایی (نفر اول)