A Remarkable Property of Concircular Vector Fields on a Riemannian Manifold
Abstract
1. Introduction
2. Preliminaries
3. Connecting Functions of Concircular Vector Fields
4. Characterizations of Euclidean Spaces
5. Influence of Concircular Vector Fields on Topology
Author Contributions
Funding
Conflicts of Interest
References
- Chen, B.-Y. Some results on concircular vector fields and their applications to Ricci solitons. Bull. Korean Math. Soc. 2015, 52, 1535–1547. [Google Scholar] [CrossRef]
- Chen, B.-Y.; Deshmukh, S.; Ishan, A.A. On Jacobi-type vector fields on Riemannian manifolds. Mathematics 2019, 7, 1139. [Google Scholar] [CrossRef]
- Chen, B.-Y.; Deshmukh, S. Some results about concircular vector fields on Riemannian manifolds. Filomat 2020, 34. Available online: http://journal.pmf.ni.ac.rs/filomat/index.php/filomat/article/view/12274 (accessed on 24 February 2020).
- Deshmukh, S. Conformal Vector Fields and Eigenvectors of Laplacian Operator. Math. Phys. Anal. Geom. 2012, 15, 163–172. [Google Scholar] [CrossRef]
- Deshmukh, S.; Al-Solamy, F. Conformal gradient vector fields on a compact Riemannian manifold. Colloq. Math. 2008, 112, 157–161. [Google Scholar] [CrossRef]
- Deshmukh, S. Jacobi-type vector fields and Ricci soliton. Bull. Math. Soc. Sci. Math. Roumanie 2012, 55, 41–50. [Google Scholar]
- Deshmukh, S.; Khan, V.A. Geodesic vector fields and Eikonal equation on a Riemannian manifold. Indag. Math. 2019, 30, 542–552. [Google Scholar] [CrossRef]
- Deshmukh, S.; Turki, N. A note on φ-analytic conformal vector fields. Anal. Math. Phys. 2019, 9, 181–195. [Google Scholar] [CrossRef]
- Deshmukh, S. Characterizing spheres and Euclidean spaces by conformal vector field. Annali di Matematica Pura ed Applicata 2017, 196, 2135–2145. [Google Scholar] [CrossRef]
- Deshmukh, S.; Peška, P.; Bin Turki, N. Geodesic Vector Fields on a Riemannian Manifold. Mathematics 2020, 8, 137. [Google Scholar] [CrossRef]
- Fialkow, A. Conformal geodesics. Trans. Amer. Math. Soc. 1939, 45, 443–473. [Google Scholar] [CrossRef]
- Ishihara, S. On infinitesimal concircular transformations. Kodai Math. Sem. Rep. 1960, 12, 45–56. [Google Scholar] [CrossRef]
- Obata, M. Conformal transformations of Riemannian manifolds. J. Diff. Geom. 1970, 4, 311–333. [Google Scholar] [CrossRef]
- Obata, M. The conjectures about conformal transformations. J. Diff. Geom. 1971, 6, 247–258. [Google Scholar] [CrossRef]
- Pigola, S.; Rimoldi, M.; Setti, A.G. Remarks on non-compact gradient Ricci solitons. Math. Z. 2011, 268, 777–790. [Google Scholar] [CrossRef]
- Yano, K. Concircular geometry I. Concircular transformations. Proc. Imp. Acad. Tokyo 1940, 16, 195–200. [Google Scholar] [CrossRef]
- Shandra, I.G. Concircular vector fields on semi-Riemannian spases. J. Math. Sci. 2007, 142, 2419–2435. [Google Scholar] [CrossRef]
- Takeno, H. Concircular scalar field in spherically symmetric space-times I. Tensor 1967, 20, 167–176. [Google Scholar]
- Besse, A.L. Einstein Manifolds; Springer: Berlin/Heidelberg, Germany, 1987. [Google Scholar]
- Chen, B.-Y. Concircular vector fields and pseudo-Kaehler manifolds. Kragujevak J. Math. 2016, 40, 7–14. [Google Scholar] [CrossRef]
- Milnor, J. Differenial Topology. In Lectures on Modern Mathematics III; Saaty, T.L., Ed.; John Wiley & Sons: Hoboken, NJ, USA, 1964. [Google Scholar]
- Lee, J.M. Introduction to Smooth Manifolds; GMT-218; Springer: Berlin/Heidelberg, Germany, 2003. [Google Scholar]
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Al-Dayel, I.; Deshmukh, S.; Belova, O. A Remarkable Property of Concircular Vector Fields on a Riemannian Manifold. Mathematics 2020, 8, 469. https://doi.org/10.3390/math8040469
Al-Dayel I, Deshmukh S, Belova O. A Remarkable Property of Concircular Vector Fields on a Riemannian Manifold. Mathematics. 2020; 8(4):469. https://doi.org/10.3390/math8040469
Chicago/Turabian StyleAl-Dayel, Ibrahim, Sharief Deshmukh, and Olga Belova. 2020. "A Remarkable Property of Concircular Vector Fields on a Riemannian Manifold" Mathematics 8, no. 4: 469. https://doi.org/10.3390/math8040469
APA StyleAl-Dayel, I., Deshmukh, S., & Belova, O. (2020). A Remarkable Property of Concircular Vector Fields on a Riemannian Manifold. Mathematics, 8(4), 469. https://doi.org/10.3390/math8040469