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In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean (n + 1)-space ${\mathbb{E}}^{n+1}$. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$ respectively. We have shown that the generalized spherical surfaces of first kind in ${\mathbb{E}}^4$ are known as rotational surfaces, and the second kind generalized spherical surfaces are known as meridian surfaces in ${\mathbb{E}}^4$. We have also calculated the Gaussian, normal and mean curvatures of these kind of surfaces. Finally, we give some examples.
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참고문헌 (20)
참고문헌 신청
K. Arslan / 2012 / General Rotation Surfaces in E4 / Results. Math 61:315~327
Kadri Arslan / 2014 / MERIDIAN SURFACES IN E4 WITH POINTWISE 1-TYPE GAUSS MAP / 대한수학회보 51(3):911~922
K. Arslan / 2011 / Rotational Embeddings in E4 with Pointwise 1-type Gauss Map / Turk. J. Math. 35:493~499
B. Bulca / 2012 / Spherical Product Surfaces in E4 / An. St. Univ. Ovidius Constanta 20:41~54
B. Bulca / 2009 / Spherical Product Surfaces in E3 / Int. Conference on CYBERWORLDS :132~137
Kadri Arslan / 2014 / MERIDIAN SURFACES IN E4 WITH POINTWISE 1-TYPE GAUSS MAP / 대한수학회보 51(3):911~922
K. Arslan / 2011 / Rotational Embeddings in E4 with Pointwise 1-type Gauss Map / Turk. J. Math. 35:493~499
B. Bulca / 2012 / Spherical Product Surfaces in E4 / An. St. Univ. Ovidius Constanta 20:41~54
B. Bulca / 2009 / Spherical Product Surfaces in E3 / Int. Conference on CYBERWORLDS :132~137
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