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CONTACT CR-WARPED PRODUCT SUBMANIFOLDS IN KENMOTSU SPACE FORMS
ARSLAN, KADRI,EZENTAS, RIDVAN,MIHAl, ION,MURATHAN, CENGIZHAN Korean Mathematical Society 2005 대한수학회지 Vol.42 No.5
Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.
ON GENERALIZED ROTATIONAL SURFACES IN EUCLIDEAN SPACES
Kadri ARSLAN,Betul Bulca,Didem Kosova 대한수학회 2017 대한수학회지 Vol.54 No.3
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.
TENSOR PRODUCT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP
Arslan, Kadri,Bulca, Betul,Kilic, Bengu,Kim, Young-Ho,Murathan, Cengizhan,Ozturk, Gunay Korean Mathematical Society 2011 대한수학회보 Vol.48 No.3
Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ to have pointwise 1-type Gauss map.
Tensor product surfaces with pointwise 1-type Gauss map
Kadri Arslan,Betul Bulca,Bengu Kilic,Young Ho Kim,Cengizhan Murathan,Gunay Ozturk 대한수학회 2011 대한수학회보 Vol.48 No.3
Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle c_1 centered at origin with an Euclidean planar curve c_2 has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle c_1 centered at origin with an Euclidean planar curve c_2 to have pointwise 1-type Gauss map.
Contact CR-Warped Product Submanifolds in Kenmotsu Space Forms
Kadri Arslan 대한수학회 2005 대한수학회지 Vol.42 No.5
Recently, Chen studied warped products which are CR-submanifoldsin Kaehler manifolds and established general sharp inequalities for CR%-warped products in Kaehler manifolds. In the present paper, weobtain sharp estimates for the squared norm of the secondfundamental form (an extrinsic invariant) in terms of the warpingfunction for contact CR-warped products isometrically immersedin Kenmotsu space forms. The equality case is considered. Some applications are derived.
ON GENERALIZED ROTATIONAL SURFACES IN EUCLIDEAN SPACES
Arslan, Kadri,Bulca, Betul,Kosova, Didem Korean Mathematical Society 2017 대한수학회지 Vol.54 No.3
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.
MERIDIAN SURFACES IN <sup>4</sup> WITH POINTWISE 1-TYPE GAUSS MAP
Arslan, Kadri,Bulca, Betul,Milousheva, Velichka Korean Mathematical Society 2014 대한수학회보 Vol.51 No.3
In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We show that a meridian surface has a harmonic Gauss map if and only if it is part of a plane. Further, we give necessary and sufficient conditions for a meridian surface to have pointwise 1-type Gauss map and find all meridian surfaces with pointwise 1-type Gauss map.
CHARACTERIZATIONS OF SPACE CURVES WITH 1-TYPE DARBOUX INSTANTANEOUS ROTATION VECTOR
Arslan, Kadri,Kocayigit, Huseyin,Onder, Mehmet Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.2
In this study, by using Laplace and normal Laplace operators, we give some characterizations for the Darboux instantaneous rotation vector field of the curves in the Euclidean 3-space $E^3$. Further, we give necessary and sufficient conditions for unit speed space curves to have 1-type Darboux vectors. Moreover, we obtain some characterizations of helices according to Darboux vector.
MERIDIAN SURFACES IN E4 WITH POINTWISE 1-TYPE GAUSS MAP
Kadri Arslan,Betul Bulca,Velichka Milousheva 대한수학회 2014 대한수학회보 Vol.51 No.3
In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We show that a meridian surface has a harmonic Gauss map if and only if it is part of a plane. Further, we give necessary and sufficient conditions for a meridian surface to have pointwise 1-type Gauss map and find all meridian surfaces with pointwise 1-type Gauss map.
ON GENERALIZED SPHERICAL SURFACES IN EUCLIDEAN SPACES
Bayram, Bengu,Arslan, Kadri,Bulca, Betul The Honam Mathematical Society 2017 호남수학학술지 Vol.39 No.3
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.