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Displaying 401 – 420 of 554

Sharp eigenvalue estimates of closed $H$ -hypersurfaces in locally symmetric spaces

Eudes L. de Lima, Henrique F. de Lima, Fábio R. dos Santos, Marco A. L. Velásquez (2019)

Czechoslovak Mathematical Journal

The purpose of this article is to obtain sharp estimates for the first eigenvalue of the stability operator of constant mean curvature closed hypersurfaces immersed into locally symmetric Riemannian spaces satisfying suitable curvature conditions (which includes, in particular, a Riemannian space with constant sectional curvature). As an application, we derive a nonexistence result concerning strongly stable hypersurfaces in these ambient spaces.

Simons Type Equation in $𝕊^{2} \times ℝ$ and $ℍ^{2} \times ℝ$ and Applications

Márcio Henrique Batista da Silva (2011)

Annales de l’institut Fourier

Let $Σ^{2}$ be an immersed surface in $M^{2} (c) \times ℝ$ with constant mean curvature. We consider the traceless Weingarten operator $φ$ associated to the second fundamental form of the surface, and we introduce a tensor $S$ , related to the Abresch-Rosenberg quadratic differential form. We establish equations of Simons type for both $φ$ and $S$ . By using these equations, we characterize some immersions for which $| φ |$ or $| S |$ is appropriately bounded.

Simultaneous unitarizability of SL $_{n} ℂ$ -valued maps, and constant mean curvature k-noid monodromy

Wayne Rossman, Nicholas Schmitt (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We give necessary and sufficient local conditions for the simultaneous unitarizability of a set of analytic matrix maps from an analytic 1-manifold into ${SL}_{n} ℂ$ under conjugation by a single analytic matrix map.We apply this result to the monodromy arising from an integrable partial differential equation to construct a family of $k$ -noids, genus-zero constant mean curvature surfaces with three or more ends in euclidean, spherical and hyperbolic $3$ -spaces.

Slant submanifolds in cosymplectic manifolds

Ram Shankar Gupta, S. M. Khursheed Haider, A. Sharfuddin (2006)

Colloquium Mathematicae

We give some examples of slant submanifolds of cosymplectic manifolds. Also, we study some special slant submanifolds, called austere submanifolds, and establish a relation between minimal and anti-invariant submanifolds which is based on properties of the second fundamental form. Moreover, we give an example to illustrate our result.

Slant submanifolds with prescribed scalar curvature into cosymplectic space form.

Gupta, Ram Shankar, Haider, S.M.Khrusheed, Sharfuddin, A. (2006)

Balkan Journal of Geometry and its Applications (BJGA)

Slant surfaces with prescribed Gaussian curvature.

Chen, Bang-Yen, Vrancken, Luc (2002)

Balkan Journal of Geometry and its Applications (BJGA)

Sobre inmersiones isométricas de variedades rienmmannianas en espacios euclideos.

Carlos Curras Bosch (1977)

Collectanea Mathematica

Some 2-type submanifolds and applications

Bang-Yen Chen, Huei-Shyong Lue (1988)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Some existence and uniqueness theorems for doubly periodic minimal surfaces.

Fusheng Wei (1992)

Inventiones mathematicae

Some inequalities for immersed surfaces.

Marenich, V., Guadalupe, I.V. (1997)

Portugaliae Mathematica

Some nonexistence theorems on stable minimal submanifolds

Haizhong Li (1997)

Colloquium Mathematicae

We prove that there exist no stable minimal submanifolds in some n-dimensional ellipsoids, which generalizes J. Simons' result about the unit sphere and gives a partial answer to Lawson–Simons' conjecture.

Some recent developments in the theory of properly embedded minimal surfaces in $ℝ^{3}$

Harold Rosenberg (1991/1992)

Séminaire Bourbaki

Some Remarks on a Class of Submanifolds in Space Forms of Non-Negative Curvature.

Kinetsu Abe (1980)

Mathematische Annalen

Some remarks on the Kozlowski-Simon conjecture for affine ovaloids

Zejun Hu, Guosong Zhao (2005)

Banach Center Publications

In this note, we are concerned with the Kozlowski-Simon conjecture on ovaloids and prove that it is correct under additional conditions.

In this paper, we get an intrinsic inequality for spacelike submanifolds in indefinite space form $M_{p}^{n + p} (c)$ , $(c > 0)$ . We also get some rigidity theorems for such spacelike submanifolds.

Currently displaying 401 – 420 of 554

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