A note on conformal vector fields on a Riemannian manifold

Sharief Deshmukh, and Falleh Al-Solamy. "A note on conformal vector fields on a Riemannian manifold." Colloquium Mathematicae 136.1 (2014): 65-73. <http://eudml.org/doc/283610>.

@article{ShariefDeshmukh2014,
abstract = {We consider an n-dimensional compact Riemannian manifold (M,g) and show that the presence of a non-Killing conformal vector field ξ on M that is also an eigenvector of the Laplacian operator acting on smooth vector fields with eigenvalue λ > 0, together with an upper bound on the energy of the vector field ξ, implies that M is isometric to the n-sphere Sⁿ(λ). We also introduce the notion of φ-analytic conformal vector fields, study their properties, and obtain a characterization of n-spheres using these vector fields.},
author = {Sharief Deshmukh, Falleh Al-Solamy},
journal = {Colloquium Mathematicae},
keywords = {conformal vector fields; Obata's theorem; -analytic conformal vector fields},
language = {eng},
number = {1},
pages = {65-73},
title = {A note on conformal vector fields on a Riemannian manifold},
url = {http://eudml.org/doc/283610},
volume = {136},
year = {2014},
}

TY - JOUR
AU - Sharief Deshmukh
AU - Falleh Al-Solamy
TI - A note on conformal vector fields on a Riemannian manifold
JO - Colloquium Mathematicae
PY - 2014
VL - 136
IS - 1
SP - 65
EP - 73
AB - We consider an n-dimensional compact Riemannian manifold (M,g) and show that the presence of a non-Killing conformal vector field ξ on M that is also an eigenvector of the Laplacian operator acting on smooth vector fields with eigenvalue λ > 0, together with an upper bound on the energy of the vector field ξ, implies that M is isometric to the n-sphere Sⁿ(λ). We also introduce the notion of φ-analytic conformal vector fields, study their properties, and obtain a characterization of n-spheres using these vector fields.
LA - eng
KW - conformal vector fields; Obata's theorem; -analytic conformal vector fields
UR - http://eudml.org/doc/283610
ER -