Results 11 to 20 of about 1,494 (50)

Constant mean curvature hypersurfaces with constant δ‐invariant

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 67, Page 4205-4216, 2003., 2003
We completely classify constant mean curvature hypersurfaces (CMC) with constant δ‐invariant in the unit 4‐sphere S4 and in the Euclidean 4‐space 𝔼4.
Bang-Yen Chen, Oscar J. Garay
wiley   +1 more source

Super parallel immersions in Euclidean space

International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 1, Page 1-5, 2002., 2002
Two submanifolds of Euclidean n‐space En are called super parallel if the affine normal spaces are homothetic at the corresponding points. Characterizations are given for the action of conformal transformation on super parallel mates. Our notion is generalized to super transnormal submanifolds and its relation with super self‐parallel submanifolds and ...
Tarek Fathy Mersal, Mohamed Esmail Basher   +1 more
wiley   +1 more source

First eigenvalue of submanifolds in Euclidean space

International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 1, Page 43-48, 2000., 2000
We give some estimates of the first eigenvalue of the Laplacian for compact and non‐compact submanifold immersed in the Euclidean space by using the square length of the second fundamental form of the submanifold merely. Then some spherical theorems and a nonimmersibility theorem of Chern and Kuiper type can be obtained.
Kairen Cai
wiley   +1 more source

Parallel Mean Curvature Surfaces in Symmetric Spaces

, 2011
We present a reduction of codimension theorem for surfaces with parallel mean curvature in symmetric ...
H. Alencar, Maria João Ferreira, R. Eschenburg, Renato Tribuzy, S.-T. Yau   +4 more
core   +1 more source

A Remark on Soliton Equation of Mean Curvature Flow

, 2003
In this short note, we consider self-similar immersions $F: \mathbb{R}^n \to \mathbb{R}^{n+k}$ of the Graphic Mean Curvature Flow of higher co-dimension.
Ma, L., Yang, Y.
core   +5 more sources

Lagrangian geometry of the Gauss images of isoparametric hypersurfaces in spheres

Complex Manifolds, 2019
The Gauss images of isoparametric hypersufaces of the standard sphere Sn+1 provide a rich class of compact minimal Lagrangian submanifolds embedded in the complex hyperquadric Qn(ℂ).
Miyaoka Reiko, Ohnita Yoshihiro
doaj   +1 more source

Unique isometric immersion into hyperbolic space

, 1992
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 4, Page 725-732, 1993.
M. Beltagy
wiley   +1 more source

On constant higher order mean curvature hypersurfaces in Hn×R ${\mathbb{H}}^{n}{\times}\mathbb{R}$

Advanced Nonlinear Studies
We classify hypersurfaces with rotational symmetry and positive constant r-th mean curvature in Hn×R ${\mathbb{H}}^{n}{\times}\mathbb{R}$ . Specific constant higher order mean curvature hypersurfaces invariant under hyperbolic translation are also ...
Nelli Barbara, Pipoli Giuseppe, Russo Giovanni   +2 more
doaj   +1 more source

Corrigendum for "A geometric proof of the Karpelevich-Mostow theorem" [PDF]

, 2016
Corollary 2.3 in our paper "A geometric proof of the Karpelevich-Mostow theorem", Bull. Lond. Math. Soc. 41 (2009), no. 4, 634-638, is false. Here we give a counterexample and show how to avoid the use of this corollary to give a simpler proof of ...
Di Scala, Antonio J., Olmos, Carlos
core  

Chen's conjecture and epsilon-superbiharmonic submanifolds of Riemannian manifolds

, 2013
B.-Y. Chen famously conjectured that every submanifold of Euclidean space with harmonic mean curvature vector is minimal. In this note we establish a much more general statement for a large class of submanifolds satisfying a growth condition at infinity.
Wheeler, Glen
core   +1 more source