Geodesic
Geometric characterizations of canal hypersurfaces in Euclidean spaces
Filomat, Tome 37 (2023) no. 18, p. 5909

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DOI

In the present paper, firstly we obtain the general expression of canal hypersurfaces in Euclidean n-space and deal with canal hypersurfaces in Euclidean 4-space E4. We compute Gauss map, Gaussian curvature and mean curvature of canal hypersurfaces in E4 and obtain an important relation between the mean and Gaussian curvatures as 3Hρ = Kρ3 − 2. We prove that, the flat canal hypersurfaces in Euclidean 4-space are only circular hypercylinders or circular hypercones and minimal canal hypersurfaces are only generalized catenoids. Also, we state the expression of tubular hypersurfaces in Euclidean spaces and give some results about Weingarten tubular hypersurfaces in E4.
DOI : 10.2298/FIL2318909K
Classification : 14J70, 53A07, 53A10
Keywords: Canal hypersurface, Tubular hypersurface, Mean curvature 
Ahmet Kazan; Mustafa Altın; Dae Won Yoon. Geometric characterizations of canal hypersurfaces in Euclidean spaces. Filomat, Tome 37 (2023) no. 18, p. 5909 . doi: 10.2298/FIL2318909K
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     title = {Geometric characterizations of canal hypersurfaces in {Euclidean} spaces},
     journal = {Filomat},
     pages = {5909 },
     year = {2023},
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     doi = {10.2298/FIL2318909K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2318909K/}
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