کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8255869 | 1533715 | 2018 | 42 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Twistor interpretation of slice regular functions
ترجمه فارسی عنوان
تفسیر تویستور از توابع منظم برش
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
چکیده انگلیسی
Given a slice regular function f:ΩâHâH, with Ωâ©Râ â
, it is possible to lift it to surfaces in the twistor space CP3 of S4âHâª{â} (see Gentili et al., 2014). In this paper we show that the same result is true if one removes the hypothesis Ωâ©Râ â
on the domain of the function f. Moreover we find that if a surface SâCP3 contains the image of the twistor lift of a slice regular function, then S has to be ruled by lines. Starting from these results we find all the projective classes of algebraic surfaces up to degree 3 in CP3 that contain the lift of a slice regular function. In addition we extend and further explore the so-called twistor transform, that is a curve in Gr2(C4) which, given a slice regular function, returns the arrangement of lines whose lift carries on. With the explicit expression of the twistor lift and of the twistor transform of a slice regular function we exhibit the set of slice regular functions whose twistor transform describes a rational line inside Gr2(C4), showing the role of slice regular functions not defined on R. At the end we study the twistor lift of a particular slice regular function not defined over the reals. This example shows the effectiveness of our approach and opens some questions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 123, January 2018, Pages 184-208
Journal: Journal of Geometry and Physics - Volume 123, January 2018, Pages 184-208
نویسندگان
Amedeo Altavilla,