Results 21 to 30 of about 1,494 (50)

Coding of hypersurfaces in Euclidean spaces by a constant vector

Open Mathematics
An nn-dimensional Riemannian manifold (Nn,g)({N}^{n},g) isometrically immersed in Euclidean space Rn+1{R}^{n+1} with unit normal ζ\zeta and shape operator SS, for a fixed constant unit vector a→\overrightarrow{{\bf{a}}} in Rn+1{R}^{n+1} induces a vector
Deshmukh Sharief, Guediri Mohammed
doaj   +1 more source

Embedded constant curvature curves on convex surfaces

, 2011
We prove the existence of embedded closed constant curvature curves on convex surfaces.Comment: 6 ...
Rosenberg, Harold, Schneider, Matthias
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On the umbilic set of immersed surfaces in three-dimensional space forms

, 2019
We prove that under some assumptions on the mean curvature the set of umbilical points of an immersed surface in a $3$-dimensional space form has positive measure. In case of an immersed sphere our result can be seen as a generalization of the celebrated
Catino, Giovanni, Roncoroni, Alberto, Vezzoni, Luigi   +2 more
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Survey on real forms of the complex A2(2)-Toda equation and surface theory

Complex Manifolds, 2019
The classical result of describing harmonic maps from surfaces into symmetric spaces of reductive Lie groups [9] states that the Maurer-Cartan form with an additional parameter, the so-called loop parameter, is integrable for all values of the loop ...
Dorfmeister Josef F., Freyn Walter, Kobayashi Shimpei, Wang Erxiao   +3 more
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f-biharmonic and bi-f-harmonic submanifolds of generalized (k, µ)-space-forms

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
Here we have studied f-biharmonic and bi-f-harmonic submanifolds of generalized (k, µ)-space-forms and obtained a necessary and sufficient condition on a submanifold of generalized (k, µ)-space-form to be f-biharmonic and bi-f-harmonic submanifold.
Hui Shyamal Kumar, Breaz Daniel, Mandal Pradip   +2 more
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Sphere-foliated minimal and constant mean curvature hypersurfaces in product spaces [PDF]

, 2010
In this paper, we prove that minimal hypersurfaces when $n\geq 3$ and nonzero constant mean curvature hypersurfaces when $n\geq2$ foliated by spheres in parallel horizontal hyperplanes in ${\mathbb{H}}^n \times \mathbb{R}$ must be rotationally symmetric ...
Seo, Keomkyo
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Nonexistence of mean curvature flow solitons with polynomial volume growth immersed in certain semi-Riemannian warped products

Advances in Nonlinear Analysis
Our purpose is to establish nonexistence results concerning complete noncompact mean curvature flow solitons with polynomial volume growth immersed in certain semi-Riemannian warped products, under mild constraints on the warping and soliton functions ...
Batista Márcio, Molica Bisci Giovanni, de Lima Henrique F., Gomes Wallace F.   +3 more
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Minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces

Complex Manifolds, 2019
An R-space is a compact homogeneous space obtained as an orbit of the isotropy representation of a Riemannian symmetric space. It is known that each R-space has the canonical embedding into a Kähler C-space as a real form, and thus a compact embedded ...
Ohnita Yoshihiro
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A geometric proof of the Karpelevich-Mostow's theorem

, 2007
In this paper we give a geometric proof of the Karpelevich's theorem that asserts that a semisimple Lie subgroup of isometries, of a symmetric space of non compact type, has a totally geodesic orbit.
Di Scala, Antonio J., Olmos, Carlos
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An eigenvalue estimate for self-shrinkers in a Ricci shrinker

Advanced Nonlinear Studies
In this paper, we study the drifted Laplacian Δf on a hypersurface M in a Ricci shrinker (M̄,g,f) $\left(\bar{M},g,f\right)$ . We prove that the spectrum of Δf is discrete for immersed hypersurfaces with bounded weighted mean curvature in a Ricci ...
Conrado Franciele, Zhou Detang
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