On a differential equation characterizing Euclidean spheres.

DOI10.1016/S0022-0396(03)00173-6zbMath1058.53027OpenAlexW1988739256MaRDI QIDQ1414006

Bülent Ünal, Eduardo García-Río, Demir N. Kupeli

Publication date: 19 November 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-0396(03)00173-6

zbMATH Keywords

LaplacianEuclidean sphereconformal vector fieldAffine\(k\)-Nullity vector fieldConformal vector fieldProjective vector fieldSecond covariant differential

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60)

Related Items (22)

Characterizations of Euclidean spheres ⋮ The base of warped product submanifolds of Sasakian space forms characterized by differential equations ⋮ On Obata theorem in Randers spaces ⋮ Ricci curvature of contact CR-warped product submanifolds in generalized Sasakian space forms admitting a trans-Sasakian structure ⋮ Ricci tensors on trans-Sasakian 3-manifolds ⋮ Characterizing spheres and Euclidean spaces by conformal vector fields ⋮ Characterizing small spheres in a unit sphere by Fischer-Marsden equation ⋮ Conformal vector fields on Kaehler manifolds ⋮ Application of Bochner formula to generalized Sasakian space forms ⋮ Real hypersurfaces of a complex space form ⋮ The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds ⋮ Ricci curvature for warped product submanifolds of Sasakian space forms and its applications to differential equations ⋮ Geometry of conformal vector fields ⋮ Study of differential equations on warped product semi-invariant submanifolds of the generalized Sasakian space forms ⋮ A note on \(\varphi \)-analytic conformal vector fields ⋮ Conformal vector fields and eigenvectors of Laplacian operator ⋮ Unnamed Item ⋮ On differential equations classifying a warped product submanifold of cosymplectic space forms ⋮ Conformal vector fields and the de-Rham Laplacian on a Riemannian manifold with boundary ⋮ Ricci curvature on warped product submanifolds in spheres with geometric applications ⋮ A note on some remarkable differential equations on a Riemannian manifold ⋮ The spectral theory of the Yano rough Laplacian with some of its applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a differential equation characterizing a Riemannian structure of a manifold
• On the characterization of complex projective space by differential equations
• Some differential equations on Riemannian manifolds
• A characterization of complex projective space up to biholomorphic isometry
• Characterizing specific Riemannian manifolds by differential equations
• The K-nullity spaces of the curvature operator
• Certain conditions for a Riemannian manifold to be isometric with a sphere
• Complete Riemannian Manifolds and Some Vector Fields
• Riemannian geometry
• Totally geodesic foliations

This page was built for publication: On a differential equation characterizing Euclidean spheres.