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
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
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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
Journal: Differential Geometry and its Applications - Volume 30, Issue 6, December 2012, Pages 588-603
نویسندگان
Marianty Ionel, Thomas Ivey,