This article is cited in 2 papers

A Criterion for the Concircular Mobility of Quasi-Sasakian Manifolds

V. F. Kirichenko, E. A. Pol'kina

Moscow State Pedagogical University

Abstract: The following question is considered: Which quasi-Sasakian (cosymplectic, Sasakian, or proper quasi-Sasakian) structures admit nontrivial concircular transformations of their metrics (i.e., determine Fialkow spaces), and under what conditions. It is proved that any cosymplectic manifold is a Fialkow space. Necessary and sufficient conditions for a Sasakian or a quasi-Sasakian manifold to be a Fialkow space are obtained. A fairly large class of Sasakian manifolds which are not Fialkow spaces is described.

Keywords: quasi-Sasakian structure, concircular transformation of a metric, Fialkow space, cosymplectic manifold, Sasakian manifold, Kenmotsu manifold.

UDC: 514.76

Received: 16.09.2008

DOI: 10.4213/mzm5155

 English version: Mathematical Notes, 2009, 86:3, 349–356

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