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Infinitesimal bending of a subspace of a space with non-symmetric basic tensor

Svetislav M. Minčić, Ljubica S. Velimirović (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this work infinitesimal bending of a subspace of a generalized Riemannian space (with non-symmetric basic tensor) are studied. Based on non-symmetry of the connection, it is possible to define four kinds of covariant derivative of a tensor. We have obtained derivation formulas of the infinitesimal bending field and integrability conditions of these formulas (equations).

Invariant harmonic unit vector fields on the oscillator groups

Na Xu, Ju Tan (2019)

Czechoslovak Mathematical Journal

We find all the left-invariant harmonic unit vector fields on the oscillator groups. Besides, we determine the associated harmonic maps from the oscillator group into its unit tangent bundle equipped with the associated Sasaki metric. Moreover, we investigate the stability and instability of harmonic unit vector fields on compact quotients of four dimensional oscillator group G 1 ( 1 ) .

Invariants and flow geometry

J. González-Dávila, L. Vanhecke (1999)

Colloquium Mathematicae

We continue the study of Riemannian manifolds (M,g) equipped with an isometric flow ξ generated by a unit Killing vector field ξ. We derive some new results for normal and contact flows and use invariants with respect to the group of ξ-preserving isometries to charaterize special (M,g, ξ ), in particular Einstein, η-Einstein, η-parallel and locally Killing-transversally symmetric spaces. Furthermore, we introduce curvature homogeneous flows and flow model spaces and derive an algebraic characterization...

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