A symplectic reduction for pseudo-Riemannian manifolds with compatible almost product structures.
Tensorial version of the calculus of variations.
Natural first order Lagrangians for immersions
We define natural first order Lagrangians for immersions of Riemannian manifolds and we prove a bijective correspondence between such Lagrangians and the symmetric functions on an open subset of m-dimensional Euclidean space.
On harmonic vector fields.
A tangent bundle to a Riemannian manifold carries various metrics induced by a Riemannian tensor. We consider harmonic vector fields with respect to some of these metrics. We give a simple proof that a vector field on a compact manifold is harmonic with respect to the Sasaki metric on TM if and only if it is parallel. We also consider the metrics and on a tangent bundle (cf. [YI]) and harmonic vector fields generated by them.
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