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R. Tojeiro (2010)
On a class of hypersurfaces in $$ \mathbb{S} $$n × ℝ and ℍn × ℝBulletin of the Brazilian Mathematical Society, New Series, 41
F. Dillen, M. Munteanu, J. Veken, L. Vrancken (2011)
Classification of constant angle surfaces in a warped productBalkan Journal of Geometry and Its Applications, 16
Bang‐Yen Chen (2003)
When Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane?The American Mathematical Monthly, 110
M. Munteanu, A. Nistor (2008)
A New Approach on Constant Angle Surfaces in E 3Turkish Journal of Mathematics, 33
F. Dillen, Johan Fastenakels, Joeri Veken, L. Vrancken (2007)
Constant angle surfaces in $ {\Bbb S}^2\times {\Bbb R} $Monatshefte für Mathematik, 152
F Dillen, J Fastenakels, J Veken (2009)
Surfaces in $\mathbb{S}^2 \times \mathbb{R}$ × ℝ with a canonical principal directionAnn. Global Anal. Geom., 35
F. Dillen, M. Munteanu, A. Nistor (2011)
CANONICAL COORDINATES AND PRINCIPAL DIRECTIONS FOR SURFACES IN $\mathbb{H}^2 × \mathbb{R}$Taiwanese Journal of Mathematics, 15
K. Boyadzhiev (2007)
Equiangular Surfaces, Self-Similar Surfaces, and the Geometry of SeashellsThe College Mathematics Journal, 38
B-Y Chen (2003)
Constant-ratio space-like submanifolds in pseudo-Euclidean spaceHouston J. Math., 29
F Dillen, J Fastenakels, J V d Veken, L Vrancken (2007)
Constant angle surfaces in $\mathbb{S}^2 \times \mathbb{R}$ × ℝMonatsh. Math., 152
K Kenmotsu (1980)
Surfaces of revolution with prescribed mean curvatureTôhoku Math. J., 32
Johan Fastenakels, M. Munteanu, J. Veken (2009)
Constant angle surfaces in the Heisenberg groupActa Mathematica Sinica, English Series, 27
M. Munteanu (2009)
From Golden Spirals to Constant Slope SurfacesarXiv: Differential Geometry
A. Nistor (2013)
A note on spacelike surfaces in Minkowski 3-spaceFilomat, 27
Y Fu, AI Nistor (2013)
Constant angle property and canonical principal directions for surfaces in $\mathbb{M}^2 $ (c) × ℝ1Mediter. J. Math., 10
M. Munteanu, A. Nistor (2011)
Complete classification of surfaces with a canonical principal direction in the Euclidean space $$ \mathbb{E} $$3Central European Journal of Mathematics, 9
M. Munteanu, A. Nistor (2010)
On certain surfaces in the Euclidean space ${\mathbb{E}}^3$arXiv: Differential Geometry
Bang‐Yen Chen (2002)
Convolution of Riemannian manifolds and its applicationsBulletin of the Australian Mathematical Society, 66
J. Eells (1987)
The surfaces of DelaunayThe Mathematical Intelligencer, 9
R. Tojeiro (2010)
On a class of hypersurfaces in [FORMULA]n × ℝ and ℍn × ℝBulletin of The Brazilian Mathematical Society, 41
Yu Fu, Dan Yang (2012)
On constant slope spacelike surfaces in 3-dimensional Minkowski spaceJournal of Mathematical Analysis and Applications, 385
Eugenio Garnica, O. Palmas, Gabriel Ruiz-Hern'andez (2011)
Hypersurfaces with a canonical principal directionarXiv: Differential Geometry
F Dillen, MI Munteanu, AI Nistor (2011)
Canonical coordinates and principal directions for surfaces in ℍ2 × ℝTaiwanese J. Math., 15
F. Dillen, M. Munteanu, J. Veken, L. Vrancken (2009)
Constant Angle Surfaces in a warped productarXiv: Differential Geometry
F. Dillen, M. Munteanu (2007)
Constant angle surfaces in ℍ2 × ℝBulletin of the Brazilian Mathematical Society, New Series, 40
S Haesen, AI Nistor, L Verstraelen (2012)
On Growth and Form and Geometry. IKragujevac J. Math., 36
Bang‐Yen Chen (1973)
Geometry of submanifolds
Yu Fu, Xiaoshu Wang (2013)
Classification of Timelike Constant Slope Surfaces in 3-Dimensional Minkowski SpaceResults in Mathematics, 63
Bang‐Yen Chen (2002)
Geometry of position functions of Riemannian submanifolds in pseudo-Euclidean spaceJournal of Geometry, 74
Yu Fu, A. Nistor (2013)
Constant Angle Property and Canonical Principal Directions for Surfaces in $${\mathbb{M}^{2}(c) \times {\mathbb{R}_{1}}}$$Mediterranean Journal of Mathematics, 10
B-Y Chen (2003)
More on Convolution of Riemannian ManifoldsBeiträge zur Algebra und Geometrie, 44
P. Cermelli, A. Scala (2007)
Constant-angle surfaces in liquid crystalsPhilosophical Magazine, 87
B-Y Chen (2001)
Constant-ratio hypersurfacesSoochow J. Math., 27
D'ARCY Thompson (1945)
On Growth and FormThe Journal of Philosophy, 42
R. López, M. Munteanu (2010)
On the Geometry of Constant Angle Surfaces in $Sol_3$arXiv: Differential Geometry
F. Dillen, Johan Fastenakels, J. Veken (2009)
Surfaces in $${\mathbb{S}^2\times\mathbb{R}}$$ with a canonical principal directionAnnals of Global Analysis and Geometry, 35
K. Kenmotsu (1980)
Surfaces of revolution with prescribed mean curvatureTohoku Mathematical Journal, 32
It iswell-known that the positionvector function is themost basic geometric object for a surface immersed in the three dimensional Euclidean space $\mathbb{E}^3 $ . In 2001, B.-Y. Chen defined constant ratio hypersurfaces in Euclidean n-spaces. Independently, in 2010, by using another approach in dimension 3, the second author classified constant slope surfaces. In this paper, we extend this concept in order to study surfaces with the property that the tangential component of the position vector is a principal direction on the surface.
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Apr 8, 2014
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