کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4606094 1631364 2012 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Ruled austere submanifolds of dimension four
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Ruled austere submanifolds of dimension four
چکیده انگلیسی
We classify 4-dimensional austere submanifolds in Euclidean space ruled by 2-planes. Austere submanifolds in Euclidean space were introduced by Harvey and Lawson in connection with their study of calibrated geometries. The algebraic possibilities for second fundamental forms of austere 4-folds M were classified by Bryant, falling into three types which we label A, B, and C. We show that if M is 2-ruled of Type A, then the ruling map from M into the Grassmannian of 2-planes in Rn is holomorphic, and we give a construction for M starting with a holomorphic curve in an appropriate twistor space. If M is 2-ruled of Type B, then M is either a generalized helicoid in R6 or the product of two classical helicoids in R3. If M is 2-ruled of Type C, then M is either one of the above, or a generalized helicoid in R7. We also construct examples of 2-ruled austere hypersurfaces in R5 with degenerate Gauss map.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Differential Geometry and its Applications - Volume 30, Issue 6, December 2012, Pages 588-603
نویسندگان
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