[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2018.58.2.389

From the Eisenhart Problem to Ricci Solitons in Quaternion Space Forms

Praveena, Mundalamane Manjappa (Department of Mathematics, Sri Venkateshwara College of Engineering)
Bagewadi, Channabasappa Shanthappa (Department of Mathematics, Kuvempu University)

Publication Information

Kyungpook Mathematical Journal / v.58, no.2, 2018 , pp. 389-398 More about this Journal

Abstract

In this paper we obtain the condition for the existence of Ricci solitons in nonflat quaternion space form by using Eisenhart problem. Also it is proved that if (g, V, ${\lambda}$ ) is Ricci soliton then V is solenoidal if and only if it is shrinking, steady and expanding depending upon the sign of scalar curvature. Further it is shown that Ricci soliton in semi-symmetric quaternion space form depends on quaternion sectional curvature c if V is solenoidal.

Keywords

quaternion $K{\ddot{a}}hler$ manifolds; quaternion space form; parallel second order covariant tensor field; Einstein space; Ricci soliton;

Citations & Related Records

Reference

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