# A note on conformal vector fields on a Riemannian manifold

Sharief Deshmukh; Falleh Al-Solamy

Colloquium Mathematicae (2014)

- Volume: 136, Issue: 1, page 65-73
- ISSN: 0010-1354

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topSharief 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 -

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