Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/some-characterizations-of-spheres-by-conformal-vector-fields-2n3p5L8Lxu
References (26)
-
N. Ejiri (1981)
A negative answer to a conjecture of conformal transformations of Riemannian manifoldsJournal of The Mathematical Society of Japan, 33
-
Xingwang Xu (1993)
On the existence and uniqueness of solutions of Möbius equationsTransactions of the American Mathematical Society, 337
-
K. Yano, T. Nagano (1959)
Einstein Spaces Admitting a One-Parameter Group of Conformal TransformationsNorth-holland Mathematics Studies, 70
-
Sharief Deshmukh, F. Al-Solamy (2014)
A note on conformal vector fields on a Riemannian manifoldColloquium Mathematicum, 136
-
Sharief Deshmukh (2010)
Characterizing spheres by conformal vector fieldsANNALI DELL'UNIVERSITA' DI FERRARA, 56
-
K Yano (1966)
On Riemannian manifolds with constant scalar curvature admitting a conformal transformation groupProc. Nat. Acad. Sci. USA, 55
-
K. Yano (1952)
On Harmonic and Killing Vector FieldsNorth-holland Mathematics Studies, 70
-
K Yano, T Nagano (1959)
Einstein spaces admitting a one-parameter group of conformal transformationsAnnl. Math., 69
-
J. Bourguignon, J. Ezin (1987)
Scalar curvature functions in a conformal class of metrics and conformal transformationsTransactions of the American Mathematical Society, 301
-
Sharief Deshmukh, Nasser Turki (2019)
A note on $$\varphi $$φ-analytic conformal vector fieldsAnalysis and Mathematical Physics, 9
-
矢野 健太郎 (1970)
Integral formulas in Riemannian geometry -
Libing Huang, X. Mo (2013)
On conformal fields of a Randers metric with isotropic $S$-curvatureIllinois Journal of Mathematics, 57
-
K. Yano (1966)
On riemannian manifolds with constant scalar curvature admitting a conformal transformation group.Proceedings of the National Academy of Sciences of the United States of America, 55 3
-
T. Nagano (1959)
The conformal transformation on a space with parallel Ricci tensor.Journal of The Mathematical Society of Japan, 11
-
Y. Tashiro (1965)
COMPLETE RIEMANNIAN MANIFOLDS AND SOME VECTOR FIELDSTransactions of the American Mathematical Society, 117
-
Sharief Deshmukh, F. Al-Solamy (2012)
Conformal vector fields and conformal transformations on a Riemannian manifold -
M. Obata (1962)
Certain conditions for a Riemannian manifold to be isometric with a sphereJournal of The Mathematical Society of Japan, 14
-
S Deshmukh, NB Turki (2019)
A note on ?\documentclass[12pt]{minimal}Anal. Math. Phys., 9
-
Sharief Deshmukh (2017)
Characterizing spheres and Euclidean spaces by conformal vector fieldsAnnali di Matematica Pura ed Applicata (1923 -), 196
-
D. Lüst, W. Vleeshouwers (2020)
Riemannian GeometryNature, 119
-
R. Bishop, S. Goldberg (1966)
A characterization of the Euclidean sphereBulletin of the American Mathematical Society, 72
-
Sharief Deshmukh (2011)
Characterizations of Einstein manifolds and odd-dimensional spheresJournal of Geometry and Physics, 61
-
S Deshmukh (2010)
Characterizing spheres by conformal vector fieldsAnn. Univ. Ferrara, 56
-
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
K Yano (1952)
On harmonic and Killing vector fieldsAnnal. Math., 55
-
S. Tanno, W. Weber (1969)
Closed conformal vector fieldsJournal of Differential Geometry, 3
- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s) under exclusive license to Università degli Studi di Ferrara 2022
- ISSN
- 0430-3202
- eISSN
- 1827-1510
- DOI
- 10.1007/s11565-022-00400-1
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we consider conformal characterizations of standard sphere in terms of conformal vector fields on closed Riemannian manifolds. We firstly prove that each closed Riemannian manifold with Ricci curvature being non-negative in certain direction and constant scalar curvature is isometric to standard sphere if and only if it admits a non-trivial closed conformal vector field. In the case of non-constant scalar curvature, we show that each closed Riemannian manifold of dimension two with positive Gauss curvature carrying a non-trivial closed conformal vector field is conformal to a round sphere and we generalize the result to high dimensions in two directions.
Journal
ANNALI DELL UNIVERSITA DI FERRARA – Springer Journals
Published: May 1, 2023
Keywords: Conformal vector field; Scalar curvature; Potential function; 53A30; 53C21; 58J05