This article is cited in 9 papers

Pseudo-Killing and Pseudoharmonic Vector Fields on a Riemann–Cartan Manifold

S. E. Stepanov^a, I. A. Gordeeva<sup>b

a</sup> Finance Academy under the Government of the Russian Federation
^b Vladimir State University

Abstract: Six classes of Riemann–Cartan manifolds are distinguished in an invariant way. Geometric characteristics of some of the distinguished classes of Riemann–Cartan manifolds are found, and also conditions hindering the existence, are determined. The local geometry of Riemann–Cartan manifolds carrying pseudo-Killing and pseudoharmonic vector fields is studied. Conditions hindering the existence “in the large” of pseudo-Killing and pseudoharmonic vector fields on Riemann–Cartan manifolds are obtained.

Keywords: Riemann–Cartan manifold, pseudo-Killing vector field, pseudoharmonic vector field, umbilical manifold, Ricci tensor, adjoint connection.

UDC: 514.764.22+514.764.32

Received: 11.09.2008
Revised: 11.06.2009

DOI: 10.4213/mzm6316

 English version: Mathematical Notes, 2010, 87:2, 248–257

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