On the Timelike Circular Surface and Singularities in Minkowski 3-Space
In this paper, we have parameterized a timelike (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">T</mi><mi>l</mi><mi>i</mi><mi>k...
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| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/10/989 |
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| author | Areej A. Almoneef Rashad A. Abdel-Baky |
| author_facet | Areej A. Almoneef Rashad A. Abdel-Baky |
| author_sort | Areej A. Almoneef |
| collection | DOAJ |
| description | In this paper, we have parameterized a timelike (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">T</mi><mi>l</mi><mi>i</mi><mi>k</mi><mi>e</mi></mrow></semantics></math></inline-formula>) circular surface (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">CI</mi><mspace width="4pt"></mspace><mi mathvariant="italic">surface</mi></mrow></semantics></math></inline-formula>) and have obtained its geometric properties, including striction curves, singularities, Gaussian and mean curvatures. Afterward, the situation for a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">T</mi><mi>l</mi><mi>i</mi><mi>k</mi><mi>e</mi></mrow></semantics></math></inline-formula> roller coaster surface (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">RCO</mi><mspace width="4pt"></mspace><mi mathvariant="italic">surface</mi></mrow></semantics></math></inline-formula>) to be a flat or minimal surface is examined in detail. Further, we illustrate the approach’s outcomes with a number of pertinent examples. |
| first_indexed | 2024-03-10T21:26:49Z |
| format | Article |
| id | doaj.art-ccd168af26124b0ca936adfdb5434939 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T21:26:49Z |
| publishDate | 2023-10-01 |
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| record_format | Article |
| series | Axioms |
| spelling | doaj.art-ccd168af26124b0ca936adfdb54349392023-11-19T15:38:55ZengMDPI AGAxioms2075-16802023-10-01121098910.3390/axioms12100989On the Timelike Circular Surface and Singularities in Minkowski 3-SpaceAreej A. Almoneef0Rashad A. Abdel-Baky1Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, EgyptIn this paper, we have parameterized a timelike (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">T</mi><mi>l</mi><mi>i</mi><mi>k</mi><mi>e</mi></mrow></semantics></math></inline-formula>) circular surface (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">CI</mi><mspace width="4pt"></mspace><mi mathvariant="italic">surface</mi></mrow></semantics></math></inline-formula>) and have obtained its geometric properties, including striction curves, singularities, Gaussian and mean curvatures. Afterward, the situation for a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">T</mi><mi>l</mi><mi>i</mi><mi>k</mi><mi>e</mi></mrow></semantics></math></inline-formula> roller coaster surface (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">RCO</mi><mspace width="4pt"></mspace><mi mathvariant="italic">surface</mi></mrow></semantics></math></inline-formula>) to be a flat or minimal surface is examined in detail. Further, we illustrate the approach’s outcomes with a number of pertinent examples.https://www.mdpi.com/2075-1680/12/10/989striction curvesingularitiestimelike roller coaster surfaces |
| spellingShingle | Areej A. Almoneef Rashad A. Abdel-Baky On the Timelike Circular Surface and Singularities in Minkowski 3-Space Axioms striction curve singularities timelike roller coaster surfaces |
| title | On the Timelike Circular Surface and Singularities in Minkowski 3-Space |
| title_full | On the Timelike Circular Surface and Singularities in Minkowski 3-Space |
| title_fullStr | On the Timelike Circular Surface and Singularities in Minkowski 3-Space |
| title_full_unstemmed | On the Timelike Circular Surface and Singularities in Minkowski 3-Space |
| title_short | On the Timelike Circular Surface and Singularities in Minkowski 3-Space |
| title_sort | on the timelike circular surface and singularities in minkowski 3 space |
| topic | striction curve singularities timelike roller coaster surfaces |
| url | https://www.mdpi.com/2075-1680/12/10/989 |
| work_keys_str_mv | AT areejaalmoneef onthetimelikecircularsurfaceandsingularitiesinminkowski3space AT rashadaabdelbaky onthetimelikecircularsurfaceandsingularitiesinminkowski3space |