Displaying similar documents to “Nets on a Riemannian manifold and finite-dimensional approximations of the Laplacian”

Geometry of manifolds which admit conservation laws

David E. Blair, Alexander P. Stone (1971)

Annales de l'institut Fourier


Let M be an ( n + 1 ) -dimensional Riemannian manifold admitting a covariant constant endomorphism h of the localized module of 1-forms with distinct non-zero eigenvalues. After it is shown that M is locally flat, a manifold N immersed in M is studied. The manifold N has an induced structure with n of the same eigenvalues if and only if the normal to N is a fixed direction of h . Finally conditions under which N is invariant under h , N is totally geodesic and the induced structure has vanishing...

A Weitzenbôck formula for the second fundamental form of a Riemannian foliation

Paolo Piccinni (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni


Si considera la seconda forma fondamentale α di foliazioni su varietà riemanniane e si ottiene una formula per il laplaciano 2 α - Se ne deducono alcune implicazioni per foliazioni su varietà a curvatura costante.

On natural metrics on tangent bundles of Riemannian manifolds

Mohamed Tahar Kadaoui Abbassi, Maâti Sarih (2005)

Archivum Mathematicum


There is a class of metrics on the tangent bundle T M of a Riemannian manifold ( M , g ) (oriented , or non-oriented, respectively), which are ’naturally constructed’ from the base metric g [Kow-Sek1]. We call them “ g -natural metrics" on T M . To our knowledge, the geometric properties of these general metrics have not been studied yet. In this paper, generalizing a process of Musso-Tricerri (cf. [Mus-Tri]) of finding Riemannian metrics on T M from some quadratic forms on O M × m to find metrics (not necessary...

Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden-Fowler equations

Alexandru Kristály, Vicenţiu Rădulescu (2009)

Studia Mathematica


Let (M,g) be a compact Riemannian manifold without boundary, with dim M ≥ 3, and f: ℝ → ℝ a continuous function which is sublinear at infinity. By various variational approaches, existence of multiple solutions of the eigenvalue problem - Δ g ω + α ( σ ) ω = K ̃ ( λ , σ ) f ( ω ) , σ ∈ M, ω ∈ H₁²(M), is established for certain eigenvalues λ > 0, depending on further properties of f and on explicit forms of the function K̃. Here, Δ g stands for the Laplace-Beltrami operator on (M,g), and α, K̃ are smooth positive functions. These...

Tenseness of Riemannian flows

Hiraku Nozawa, José Ignacio Royo Prieto (2014)

Annales de l’institut Fourier


We show that any transversally complete Riemannian foliation of dimension one on any possibly non-compact manifold M is tense; namely, M admits a Riemannian metric such that the mean curvature form of is basic. This is a partial generalization of a result of Domínguez, which says that any Riemannian foliation on any compact manifold is tense. Our proof is based on some results of Molino and Sergiescu, and it is simpler than the original proof by Domínguez. As an application, we generalize...

Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions

Yaning Wang, Ximin Liu (2014)

Annales Polonici Mathematici


We consider an almost Kenmotsu manifold M 2 n + 1 with the characteristic vector field ξ belonging to the (k,μ)’-nullity distribution and h’ ≠ 0 and we prove that M 2 n + 1 is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a flat n-dimensional manifold, provided that M 2 n + 1 is ξ-Riemannian-semisymmetric. Moreover, if M 2 n + 1 is a ξ-Riemannian-semisymmetric almost Kenmotsu manifold such that ξ belongs to the (k,μ)-nullity distribution, we prove...

High-order angles in almost-Riemannian geometry

Ugo Boscain, Mario Sigalotti (2006-2007)

Séminaire de théorie spectrale et géométrie


Let X and Y be two smooth vector fields on a two-dimensional manifold M . If X and Y are everywhere linearly independent, then they define a Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become linearly dependent somewhere on M , then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally...