The Fourth Fundamental Form <i>IV</i> of Dini-Type Helicoidal Hypersurface in the Four Dimensional Euclidean Space
We introduce the fourth fundamental form of a Dini-type helicoidal hypersurface in the four dimensional Euclidean space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="...
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MDPI AG
2021-08-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/3/186 |
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doaj-eb02574190ce4066b774e4e29a5ffaa22021-09-25T23:44:50ZengMDPI AGAxioms2075-16802021-08-011018618610.3390/axioms10030186The Fourth Fundamental Form <i>IV</i> of Dini-Type Helicoidal Hypersurface in the Four Dimensional Euclidean SpaceErhan Güler0Department of Mathematics, Faculty of Science, Kutlubey Campus, Bartın University, 74100 Bartın, TurkeyWe introduce the fourth fundamental form of a Dini-type helicoidal hypersurface in the four dimensional Euclidean space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-struck">E</mi></mrow><mn>4</mn></msup></semantics></math></inline-formula>. We find the Gauss map of helicoidal hypersurface in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-struck">E</mi></mrow><mn>4</mn></msup></semantics></math></inline-formula>. We obtain the characteristic polynomial of shape operator matrix. Then, we compute the fourth fundamental form matrix <i>IV</i> of the Dini-type helicoidal hypersurface. Moreover, we obtain the Dini-type rotational hypersurface, and reveal its differential geometric objects.https://www.mdpi.com/2075-1680/10/3/186four dimensionDini-type helicoidal hypersurfaceGauss mapshape operatorcurvaturesfourth fundamental form |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Erhan Güler |
| spellingShingle |
Erhan Güler The Fourth Fundamental Form <i>IV</i> of Dini-Type Helicoidal Hypersurface in the Four Dimensional Euclidean Space Axioms four dimension Dini-type helicoidal hypersurface Gauss map shape operator curvatures fourth fundamental form |
| author_facet |
Erhan Güler |
| author_sort |
Erhan Güler |
| title |
The Fourth Fundamental Form <i>IV</i> of Dini-Type Helicoidal Hypersurface in the Four Dimensional Euclidean Space |
| title_short |
The Fourth Fundamental Form <i>IV</i> of Dini-Type Helicoidal Hypersurface in the Four Dimensional Euclidean Space |
| title_full |
The Fourth Fundamental Form <i>IV</i> of Dini-Type Helicoidal Hypersurface in the Four Dimensional Euclidean Space |
| title_fullStr |
The Fourth Fundamental Form <i>IV</i> of Dini-Type Helicoidal Hypersurface in the Four Dimensional Euclidean Space |
| title_full_unstemmed |
The Fourth Fundamental Form <i>IV</i> of Dini-Type Helicoidal Hypersurface in the Four Dimensional Euclidean Space |
| title_sort |
fourth fundamental form <i>iv</i> of dini-type helicoidal hypersurface in the four dimensional euclidean space |
| publisher |
MDPI AG |
| series |
Axioms |
| issn |
2075-1680 |
| publishDate |
2021-08-01 |
| description |
We introduce the fourth fundamental form of a Dini-type helicoidal hypersurface in the four dimensional Euclidean space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-struck">E</mi></mrow><mn>4</mn></msup></semantics></math></inline-formula>. We find the Gauss map of helicoidal hypersurface in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-struck">E</mi></mrow><mn>4</mn></msup></semantics></math></inline-formula>. We obtain the characteristic polynomial of shape operator matrix. Then, we compute the fourth fundamental form matrix <i>IV</i> of the Dini-type helicoidal hypersurface. Moreover, we obtain the Dini-type rotational hypersurface, and reveal its differential geometric objects. |
| topic |
four dimension Dini-type helicoidal hypersurface Gauss map shape operator curvatures fourth fundamental form |
| url |
https://www.mdpi.com/2075-1680/10/3/186 |
| work_keys_str_mv |
AT erhanguler thefourthfundamentalformiiviofdinitypehelicoidalhypersurfaceinthefourdimensionaleuclideanspace AT erhanguler fourthfundamentalformiiviofdinitypehelicoidalhypersurfaceinthefourdimensionaleuclideanspace |
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1717368152092835840 |