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Parabolicity and rigidity of spacelike hypersurfaces immersed in a Lorentzian Killing warped product

Eudes L. de Lima, Henrique F. de Lima, Eraldo A. Jr. Lima, Adriano A. Medeiros (2017)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we extend a technique due to Romero et al. establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed into a Lorentzian Killing warped product whose Riemannian base has parabolic universal Riemannian covering. As applications, we obtain rigidity results concerning these hypersurfaces. A particular study of entire Killing graphs is also made.

Parallel hypersurfaces

Barbara Opozda, Udo Simon (2014)

Annales Polonici Mathematici

We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.

Parallel immersions into spaces of constant curvature and conformal transformations.

Wegner, Bernd (1997)

General Mathematics

Parallel Kaehler Submanifolds of Hermitian Symmetric Spaces.

Kazumi Tsukada (1985)

Mathematische Zeitschrift

Particular $F$ -structure on vector bundle and compatible $D$ -connections.

Stoica, Emil (1999)

Novi Sad Journal of Mathematics

Perturbations à symétrie sphérique de la métrique d'un univers en expansion, II

A. Papapetrou (1978)

Annales de l'I.H.P. Physique théorique

Peterson's deformations of higher dimensional quadrics.

Dincă, Ion I. (2010)

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

Plateau-Stein manifolds

Misha Gromov (2014)

Open Mathematics

We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.

Poincaré-Cartan forms in higher order variational calculus on fibred manifolds.

Jaime Muñoz Masqué (1985)

Revista Matemática Iberoamericana

The aim of the present work is to present a geometric formulation of higher order variational problems on arbitrary fibred manifolds. The problems of Engineering and Mathematical Physics whose natural formulation requires the use of second order differential invariants are classic, but it has been the recent advances in the theory of integrable non-linear partial differential equations and the consideration in Geometry of invariants of increasingly higher orders that has highlighted the interest...

Polynomial translation surfaces of Weingarten types in Euclidean 3-space

Dae Yoon (2010)

Open Mathematics

In this paper, we classify polynomial translation surfaces in Euclidean 3-space satisfying the Jacobi condition with respect to the Gaussian curvature, the mean curvature and the second Gaussian curvature.