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

S. E. Stepanov ; I. A. Gordeeva

Matematičeskie zametki, Tome 87 (2010) no. 2, pp. 267-279.

Résumé

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.

Détail

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

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