[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b210125

SASAKIAN 3-METRIC AS A *-CONFORMAL RICCI SOLITON REPRESENTS A BERGER SPHERE

Dey, Dibakar (Department of Pure Mathematics University of Calcutta)

Publication Information

Bulletin of the Korean Mathematical Society / v.59, no.1, 2022 , pp. 101-110 More about this Journal

Abstract

In this article, the notion of *-conformal Ricci soliton is defined as a self similar solution of the *-conformal Ricci flow. A Sasakian 3-metric satisfying the *-conformal Ricci soliton is completely classified under certain conditions on the soliton vector field. We establish a relation with Fano manifolds and proves a homothety between the Sasakian 3-metric and the Berger Sphere. Also, the potential vector field V is a harmonic infinitesimal automorphism of the contact metric structure.

Keywords

Sasakian 3-manifold; *-conformal Ricci soliton; infinitesimal contact transformation; infinitesimal automorphism; Berger sphere; Fano manifold;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

1	Y. Aryanejad, Some geometrical properties of Berger spheres, Caspian J. Math. Sci. https://doi.org/10.22080/CJMS.2021.3055 DOI
2	C. P. Boyer, K. Galicki, and P. Matzeu, On eta-Einstein Sasakian geometry, Comm. Math. Phys. 262 (2006), no. 1, 177-208. https://doi.org/10.1007/s00220-005-1459-6 DOI
3	D. Dey and P. Majhi, -Ricci solitons and -gradient Ricci solitons on 3-dimensional trans-Sasakian manifolds, Commun. Korean Math. Soc. 35 (2020), no. 2, 625-637. https://doi.org/10.4134/CKMS.c190121 DOI
4	J. Figueroa-O'Farrill and A. Santi, Sasakian manifolds and M-theory, Classical Quantum Gravity 33 (2016), no. 9, 095004, 18 pp. https://doi.org/10.1088/0264-9381/33/9/095004 DOI
5	B. S. Guifoyle, Einstein metrics adapted to a contact structure on 3-manifolds, Preprint. arXiv:math/0012027v1 [math.DG] (2000).
6	B. S. Guifoyle, The local moduli of Sasakian 3-manifolds, Int. J. Math. Math. Sci. 32 (2002), no. 2, 117-127. https://doi.org/10.1155/S0161171202006774 DOI
7	J.-B. Jun, I. B. Kim, and U. K. Kim, On 3-dimensional almost contact metric manifolds, Kyungpook Math. J. 34 (1994), no. 2, 293-301.
8	P. Majhi, U. C. De, and Y. J. Suh, *-Ricci solitons and Sasakian 3-manifolds, Publ. Math. Debrecen 93 (2018), no. 1-2, 241-252. https://doi.org/10.5486/pmd.2018.8245 DOI
9	S. Tanno, Note on infinitesimal transformations over contact manifolds, Tohoku Math. J. (2) 14 (1962), 416-430. https://doi.org/10.2748/tmj/1178244078 DOI
10	K. Yano, Integral formulas in Riemannian geometry, Pure and Applied Mathematics, No. 1, Marcel Dekker, Inc., New York, 1970.
11	P. M. Gadea and J. A. Oubina, Homogeneous Riemannian structures on Berger 3-spheres, Proc. Edinb. Math. Soc. (2) 48 (2005), no. 2, 375-387. https://doi.org/10.1017/S0013091504000422 DOI