ON GENERALIZED ROTATIONAL SURFACES IN EUCLIDEAN SPACES
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In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized tractrices in Euclidean $ (n+1)$-space $\mathbb{E}^{n+1}$. Further, we introduce some kind of generalized rotational surfaces in Euclidean spaces $\mathbb{E}^{3}$ and $ \mathbb{E}^{4}$, respectively. We have also obtained some basic properties of generalized rotational surfaces in $\mathbb{E}^{4}$ and some results of their curvatures. Finally, we give some examples of generalized Beltrami surfaces in $\mathbb{E}^{3}$ and $\mathbb{E}^{4}$, respectively.
Abstract
In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized tractrices in Euclidean $ (n+1)$-space $\mathbb{E}^{n+1}$. Further, we introduce some kind of generalized rotational surfaces in Euclidean spaces $\mathbb{E}^{3}$ and $ \mathbb{E}^{4}$, respectively. We have also obtained some basic properties of generalized rotational surfaces in $\mathbb{E}^{4}$ and some results of their curvatures. Finally, we give some examples of generalized Beltrami surfaces in $\mathbb{E}^{3}$ and $\mathbb{E}^{4}$, respectively.
참고문헌 (20)
- Yu. A. Aminov, "Geometry of Submanifolds" (2001), Gordon & Breach Science Publ
- K. Arslan, "Rotational embeddings in E4 with pointwise 1-type Gauss map", Turkish J. Math, 35(3), pp.493~499 (2011)
- K. Arslan, "General rotation surfaces in E4", Results. Math, 61(3), pp.315~327 (2012)
- Kadri Arslan, "MERIDIAN SURFACES IN E4 WITH POINTWISE 1-TYPE GAUSS MAP", 대한수학회보, 51(3), pp.911~922 (2014), 대한수학회
- B. Bulca, "E4 deki Yuzeylerin Bir Karakterizasyonu", PhD, pp.2012
- B. Bulca, "Spherical product surfaces in E4", An. Stiint. Univ. “Ovidius” Constanta Ser. Mat, 20(1), pp.41~54 (2012)
- B. Bulca, "Spherical product surfaces in E3", IEEE Computer Society, Int. Conference on Cyberworlds (2009)
- B. Y. Chen, "Pseudo-umbilical surfaces with constant Gauss curvature", Proc. Edinburgh Math. Soc. (2), 18, pp.143~148 (1972)
- B. Y. Chen, "Geometry of Submanifolds" (1973), Dekker
- B. Y. Chen, "Geometry of Submanifolds and its Applications" (1981), Science University of Tokyo
- P. J. De Smet, "A pointwise inequality in submanifold theory", Arch. Math. (Brno), 35(2), pp.115~128 (1999)
- D. V. Cuong, "Surfaces of revolution with constant Gaussian curvature in four-space", arXiv:1205.2143v3, ~ (2012)
- U. Dursun, "General rotational surfaces in Euclidean space E4 with pointwise 1-type Gauss map", Math. Commun, 17(1), pp.71~81 (2012)
- G. Ganchev, "On the theory of surfaces in the four-dimensional Euclidean space", Kodai Math. J, 31(2), pp.183~198 (2008)
- G. Ganchev, "Invariants and Bonnet-type theorem for surfaces in R4", Cent. Eur. J. Math, 8(6), pp.993~1008 (2010)
- V. A. Gorkavyi, "Two-dimensional pseudospherical surfaces with degenerate Bianchi transformation", Ukrainian Mathematical Journal, 63(11) (2012)
- N. H. Kuiper, "Minimal total absolute curvature for immersions", Invent. Math, 10, pp.209~238 (1970)
- V. Velickovic, "On Surface of rotation of a given constant Gaussian curvature and their visualization", Proc. Conference Contemporary Geometry and Related Topics, pp.523~534 (2005)
- Y. C. Wong, "Contributions to the theory of surfaces in 4-space of constant curvature", Trans. Amer. Math. Soc, 59, pp.467~507 (1946)
- D. W. Yoon, "Some Properties of the Clifford torus as rotation surfaces", Indian J. Pure Appl. Math, 34(6), pp.907~915 (2003)