Special space curves characterized by det(α⁽³⁾,α⁽⁴⁾,α⁽⁵⁾)=0
By using the facts that the condition det(α⁽¹⁾,α⁽²⁾,α⁽³⁾)=0 characterizes a plane curve and the condition det(α⁽²⁾,α⁽³⁾,α⁽⁴⁾)=0 characterizes a curve of constant slope, we present special space curves characterized by the condition det(α⁽³⁾,α⁽⁴⁾,α⁽⁵⁾)=0, in different approaches. It is shown that the...
Збережено в:
| Дата: | 2014 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Назва видання: | Український математичний журнал |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/166467 |
| Теги: |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Special Space Curves Characterized by det(α⁽³⁾,α⁽⁴⁾,α⁽⁵⁾)=0 / S. Saracoglu // Український математичний журнал. — 2014. — Т. 66, № 4. — С. 571–576. — Бібліогр.: 6 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | By using the facts that the condition det(α⁽¹⁾,α⁽²⁾,α⁽³⁾)=0 characterizes a plane curve and the condition det(α⁽²⁾,α⁽³⁾,α⁽⁴⁾)=0 characterizes a curve of constant slope, we present special space curves characterized by the condition det(α⁽³⁾,α⁽⁴⁾,α⁽⁵⁾)=0, in different approaches. It is shown that the space curve is Salkowski if and only if det(α⁽³⁾,α⁽⁴⁾,α⁽⁵⁾)=0. The approach used in our investigation can be useful in understanding the role of the curves characterized by det(α⁽³⁾,α⁽⁴⁾,α⁽⁵⁾)=0 in differential geometry. |
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