arXiv subjects

Elif Özkara Canfes

Publications and source records attributed to Elif Özkara Canfes.

4 recordsLinked to original sources

arXiv2019

Biconservative quasi-minimal immersions into semi-Euclidean spaces

In this paper we study biconservative immersions into the semi-Riemannian space form $R^4_2(c)$ of dimension 4, index 2 and constant curvature, where $c\in\{0,-1,1\}$. First, we obtain a characterization of quasi-minimal proper biconservative immersions into $R^4_2(c)$. Then we obtain the complete classification of quasi-minimal biconservative surfaces in $R^4_2(0)=\mathbb E^4_2$. We also obtain a new class of biharmonic quasi-minimal isometric immersion into $\mathbb E^4_2$.

math.GM↗

arXiv2016

On rotational surfaces with zero mean curvature in the pseudo-Euclidean space $\mathbb{E}_2^4$

In this work, we study a class of rotational surfaces in the pseudo-Euclidean space $\mathbb{E}_2^4$ whose profile curves lie in two-dimensional planes. We solve the differential equation that characterizes the rotational surfaces with zero mean curvature to determine the profile curves of such rotational surfaces. Then, we give some explicit parametrization of maximal rotational surfaces and the timelike surfaces with zero mean curvature in $\mathbb{E}_2^4$.

math.DG↗

arXiv2015

Pseudo-spherical submanifolds with 1-type pseudo-spherical Gauss map

In this work, we study the pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify the Lorentzian surfaces in a 4-dimensional pseudo-sphere $\mathbb{S}^4_s(1)$ with index s, $s=1, 2$, and having harmonic pseudo-spherical Gauss map. Then we give a characterization theorem for pseudo-Riemannian submanifolds of a pseudo-sphere $\mathbb{S}^{m-1}_s(1)\subset\mathbb{E}^m_s$ with 1-type pseudo-spherical Gauss map, and we classify spacelike surfaces and Lorentzian surfaces in the de Sitter space $\mathbb{S}^4_1(1)\subset\mathbb{E}^5_1$ with 1-type pseudo-spherical Gauss map. Finally, according to the causal character of the mean curvature vector we obtain the classification of submanifolds of a pseudo-sphere having 1-type pseudo-spherical Gauss map with nonzero constant component in its spectral decomposition.

math.DG↗

arXiv2015

On rotational surfaces in pseudo-Euclidean space $\mathbb{E}^4_t$ with pointwise 1-type Gauss map

In this work, we study some classes of rotational surfaces in the pseudo-Euclidean space $\mathbb{E}^4_t$ with profile curves lying in 2-dimensional planes. First, we determine all such surfaces in the Minkowski 4-space $\mathbb{E}^4_1$ with pointwise 1-type Gauss map of the first kind and second kind. Then, we obtain rotational surfaces in $\mathbb{E}^4_2$ with zero mean curvature and having pointwise 1--type Gauss map of second kind.

math.DG↗