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On the Gauss mapping of hypersurfaces | ||
| Journal of Hyperstructures | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 خرداد 1405 اصل مقاله (1.77 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2025.17302.1088 | ||
| نویسنده | ||
| Ali Parsian* | ||
| Department of Mathematics, Tafresh Uniiversity, Tafresh, Iran. | ||
| چکیده | ||
| In this paper, we establish a one-to-one correspondence between some hypersurfaces and the images of them under their Gauss mappings. Then, we introduce a class of hypersurfaces, whose images under their Gauss mappings are the same. Moreover, we prove the evenness of the cardinal number of the cross section of a compact hypersurface S ⊆ Rm with a curve α:R→Rm which is nowhere tangent to S, and tends to infinity in directions ±∞. Finally, we clarify how the results, relate to existing literature on Gauss mappings of minimal or finite-type surfaces. Some illustrative examples and an application are also provided. | ||
| کلیدواژهها | ||
| compactness؛ hypersurface؛ minimal surface؛ vector field | ||
| مراجع | ||
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