# Isometric immersions into warped product spaces

## Related Articles

- Laguerre isopararmetric hypersurfaces in â„. Li, Tong; Sun, Hua // Acta Mathematica Sinica;Jun2012, Vol. 28 Issue 6, p1179
Let x: M â†’ â„ be an umbilical free hypersurface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor $\mathbb{L}$, a Laguerre form C, and a Laguerre second fundamental form $\mathbb{B}$ which are invariants of x under Laguerre...

- Local audibility of a hyperbolic metric. Sharafutdinov, V. A. // Siberian Mathematical Journal;Sep2009, Vol. 50 Issue 5, p929
A Riemannian metric g on a compact boundaryless manifold is said to be locally audible if the following statement is true for every metric g' sufficiently close to g: if g and g' are isospectral then they are isometric. The local audibility is proved of a metric of constant negative sectional...

- Most Convex Bodies are Isometrically Indivisible. Richter, Christian // Journal of Geometry;2008, Vol. 89 Issue 1/2, p130
A set C in the Euclidean space $${\mathbb{R}}^d$$ is called isometrically m-divisible if there exists a disjoint decomposition of C into m subsets C i pairwise congruent with respect to the group of Euclidean isometries. We present a necessary condition for the isometric m-divisibility, which...

- On the developable ruled surfaces of low smoothness. Sabitov, I. Kh. // Siberian Mathematical Journal;Sep2009, Vol. 50 Issue 5, p919
The classical description of the structure of developable surfaces of torse type is formally possible only starting with C3-smoothness. We consider developable surfaces of class C2 and show that the directions of their generators at the boundary points of a surface belong to the tangent cone of...

- Almost isometric actions, property ( T), and local rigidity. Fisher, David; Margulis, Gregory // Inventiones Mathematicae;Oct2005, Vol. 162 Issue 1, p19
Let G be a discrete group with property ( T) of Kazhdan. We prove that any Riemannian isometric action of G on a compact manifold X is locally rigid. We also prove a more general foliated version of this result. The foliated result is used in our proof of local rigidity for standard actions of...

- On the classification of positive quaternionic KÃ¤hler manifolds with b4 = 1. Jin Hong Kim; Hee Kwon Lee // Acta Mathematica Sinica;May2010, Vol. 26 Issue 5, p875
Let M be a positive quaternionic KÃ¤hler manifold of dimension 4 m. We already showed that if the symmetry rank is greater than or equal to $$ \left[ {\tfrac{m} {2}} \right] + 2 $$ and the fourth Betti number b4 is equal to one, then M is isometric to â„ P m. The goal of this paper is to...

- THE ADAPTED COMPLEXIFICATION OF THE TWO-SPHERE WITH A LIOUVILLE METRIC. AGUILAR, RAÚL M. // Quarterly Journal of Mathematics;Jun2009, Vol. 60 Issue 2, p133
We show that the two-sphere with a Riemannian metric that is Liouville with finite isometry group does not admit an unbounded adapted complexification in the sense of Lempert and SzÅ‘ke and of Guillemin and Stenzel; that is, its Grauert tube cannot have infinite radius. We prove this by first...

- The Generalized Pompeiu Metric in the Isometry Problem for Hyperspaces. Aseev, V. V.; Tetenov, A. V.; Maksimova, A. P. // Mathematical Notes;Jul/Aug2005, Vol. 78 Issue 1/2, p149
The isometries of the hyperspace of a compact subset of the real line endowed with the generalized Pompeiu metric are considered. It is proved that any such an isometry is generated by an isometry of the base space.

- ON THE DECOMPOSITION OF FAMILIES OF QUASINORMAL OPERATORS. Burdak, Zbigniew // Opuscula Mathematica;2013, Vol. 33 Issue 3, p419
The canonical injective decomposition of a jointly quasinormal family of operators is given. Relations between the decomposition of a quasinormal operator T and the decomposition of a partial isometry in the polar decomposition of T are described. The decomposition of pairs of commuting...