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A Weierstrass-Kenmotsu Type Representation for CMC in $\mathbb{H}^3(-1)$
Magdalena Toda, Erhan Güler, Madusha Dilhani Atampalage
We develop a Weierstrass-Kenmotsu type representation for conformal immersions of constant mean curvature in hyperbolic -space $\HH$. The construction is based on the…
Explicit Minimal Surface Models in via Holomorphic Null Curves
Magdalena Toda, Erhan Güler
We study explicit conformal minimal immersions into obtained from holomorphic null curves in . Although the general correspondence between conformal mi…
The higher-order Henneberg-type minimal surfaces family in
Erhan Güler, Magdalena Toda
We consider a higher-order Henneberg-type minimal surfaces family using the generalized Weierstrass--Enneper representation in four-dimensional space . We derive expl…
Rotational hypersurfaces family satisfying in
Erhan Güler, Nurettin Cenk Turgay
In this paper, we investigate rotational hypersurfaces family in -dimensional Euclidean space . Our focus is on studying the Gauss map of this f…
Fourth Fundamental Form and -th Curvature Formulas in
Erhan Güler
We introduce fourth fundamental form and -th curvature formulas of hypersurfaces in the four dimensional Euclidean geometry . Defining fourth fundamental…
Class, degree and integral free forms for the family of Bour's minimal surfaces
Erhan Güler
We consider the family of the Bour's minimal surfaces in Euclidean 3-space, and compute their classes, degrees and integral free representations.
A new kind of helicoidal surface of value m
Erhan Guler
We define a new kind of helicoidal surface of value m. A rotational surface which is isometric to the helicoidal surface of value m is revealed. In addition, we calculate some diff…
Bour's spacelike maximal and timelike minimal surfaces in the 3-dimensional Minkowski space
Erhan Guler
Bour's minimal surface has remarkable properties in three dimensional Minkowski space. We reveal the definite and indefinite cases of the Bour's surface using Weierstrass represent…
Isometric Surfaces and the Third Laplace-Beltrami
Erhan Güler, Yusuf Yaylı
In this paper, classical isometric helicoidal and rotational surfaces are studied, and generalized by Bour's theorem in three dimensional Euclidean space. Moreover, the third Lapla…