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In this paper we analyze the limit set of nonelementary subgroups acting by isometries on the product of two pinched Hadamard manifolds. Following M. Burger’s and P. Albuquerque’s works, we study the properties of Patterson-Sullivan’s measures on the limit sets of graph groups associated to convex cocompact groups.

Shape Operators and Structure Tensors of Real Hypersurfaces in Nonflat Quaternionic Space Forms

Sadahiro Maeda, Toshiaki Adachi (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We characterize curvature-adapted real hypersurfaces in nonflat quaternionic space forms in terms of their shape operators and structure tensors.

Shape operators of orbits of isotropy subgroups in Riemannian symmetric spaces of the compact type.

Verhóczki, László (1995)

Beiträge zur Algebra und Geometrie

Shapes of spheres of special nonholonomic left-invariant intrinsic metrics on some Lie groups.

Berestovskij, V.N., Zubareva, I.A. (2001)

Sibirskij Matematicheskij Zhurnal

Sharp bounds for the intersection of nodal lines with certain curves

Junehyuk Jung (2014)

Journal of the European Mathematical Society

Let $Y$ be a hyperbolic surface and let $φ$ be a Laplacian eigenfunction having eigenvalue $- 1 / 4 - τ^{2}$ with $τ > 0$ . Let $N (φ)$ be the set of nodal lines of $φ$ . For a fixed analytic curve $γ$ of finite length, we study the number of intersections between $N (φ)$ and $γ$ in terms of $τ$ . When $Y$ is compact and $γ$ a geodesic circle, or when $Y$ has finite volume and $γ$ is a closed horocycle, we prove that $γ$ is “good” in the sense of [TZ]. As a result, we obtain that the number of intersections between $N (φ)$ and $γ$ is $O (τ)$ . This bound is sharp.

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.

Sharp isoperimetric inequalities and model spaces for the Curvature-Dimension-Diameter condition

Emanuel Milman (2015)

Journal of the European Mathematical Society

We obtain new sharp isoperimetric inequalities on a Riemannian manifold equipped with a probability measure, whose generalized Ricci curvature is bounded from below (possibly negatively), and generalized dimension and diameter of the convex support are bounded from above (possibly infinitely). Our inequalities are sharp for sets of any given measure and with respect to all parameters (curvature, dimension and diameter). Moreover, for each choice of parameters, we identify the model spaces which...

Shells of monotone curves

Josef Mikeš, Karl Strambach (2015)

Czechoslovak Mathematical Journal

We determine in $ℝ^{n}$ the form of curves $C$ corresponding to strictly monotone functions as well as the components of affine connections $\nabla$ for which any image of $C$ under a compact-free group $Ω$ of affinities containing the translation group is a geodesic with respect to $\nabla$ . Special attention is paid to the case that $Ω$ contains many dilatations or that $C$ is a curve in $ℝ^{3}$ . If $C$ is a curve in $ℝ^{3}$ and $Ω$ is the translation group then we calculate not only the components of the curvature and the Weyl tensor but...

Shock waves and general relativity

Joel Smoller, Blake Temple (1994)

Journées équations aux dérivées partielles

Shock-wave explosions in general relativity

Elias M. Smoller, Blake Temple (1995)

Journées équations aux dérivées partielles

Shoikhet's conjecture and Duflo isomorphism on (co)invariants.

Calaque, Damien, Rossi, Carlo A. (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Sich schliessende p-Ecke aus Evoluten.

Hubert Frank (1977)

Elemente der Mathematik

Sigma models in geometry

Rocek, Martin (2004)

Proceedings of the 23rd Winter School "Geometry and Physics"

Similarity motions in $E_{3}$ with plane trajectories

Adolf Karger (1981)

Aplikace matematiky

In this paper the author finds and describes all similarity space motions, which have only plane trajectories of points. All such motions are explicitly expressed. They are of 5 types, all of them cylindrical. Trajectories are conic sections (3 types) or arbitrary plane curves (2 types).

Similarity of operators and geometry of eigenvector bundles.

H. K. Kwon, S. Treil (2009)

Publicacions Matemàtiques

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.

Simple conformally symmetric manifolds with metric semi-symmetric connection

J. Krawczyk (1988)

Colloquium Mathematicae

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