Results 11 to 20 of about 570 (49)

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
core   +1 more source

A generalization of Cartan's theorem on isoparametric cubics

, 2010
We give a generalization of the well-known result of E. Cartan on isoparametric cubics by showing that a homogeneous cubic polynomial solution of the eiconal equation $|\nabla f|^2=9|x|^4$ must be rotationally equivalent to either $x_n^3-3x_n(x_1^2 ...
Tkachev, Vladimir G.
core   +1 more source

Applications of a completeness lemma in minimal surface theory to various classes of surfaces

, 2010
We give several applications of a lemma on completeness used by Osserman to show the meromorphicity of Weierstrass data for complete minimal surfaces with finite total curvature.
Umehara, Masaaki, Yamada, Kotaro
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Minimal Darboux transformations

, 2016
We derive a permutability theorem for the Christoffel, Goursat and Darboux transformations of isothermic surfaces. As a consequence we obtain a simple proof of a relation between Darboux pairs of minimal surfaces in Euclidean space, curved flats in the 2-
Hertrich-Jeromin, U., Honda, A.
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Comparison formulas for total mean curvatures of Riemannian hypersurfaces

Advanced Nonlinear Studies
We devise some differential forms after Chern to compute a family of formulas for comparing total mean curvatures of nested hypersurfaces in Riemannian manifolds.
Ghomi Mohammad
doaj   +1 more source

Pointwise hemi-slant warped product submanifolds in nearly Kaehler manifolds

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
In this paper, we introduce the notion of pointwise hemi-slant sub-manifolds of nearly Kaehler manifolds. Further, we study their warped products and prove the necessary and sufficient condition that a point-wise hemi-slant submanifold to be a warped ...
Alqahtani Lamia Saeed, Uddin Siraj, Bossly Rawan   +2 more
doaj   +1 more source

Eigenvalue Estimates for submanifolds of $N \times \mathbb{R}$ with locally bounded mean curvature

, 2008
We give lower bounds for the fundamental tone of open sets in submanifolds with locally bounded mean curvature in $ N \times \mathbb{R}$, where $N$ is an $n$-dimensional complete Riemannian manifold with radial sectional curvature $K_{N} \leq \kappa ...
Bessa, G. Pacelli, Costa, M. Silvana
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Geometry of branched minimal surfaces of finite index

Advanced Nonlinear Studies
Given I,B∈N∪{0} $I,B\in \mathbb{N}\cup \left\{0\right\}$ , we investigate the existence and geometry of complete finitely branched minimal surfaces M in R3 ${\mathbb{R}}^{3}$ with Morse index at most I and total branching order at most B. Previous works
Meeks William H., Pérez Joaquín
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
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