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Vector fields on n-foliated 2n-dimensional manifolds

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In this paper, we study basic differential invariants of the pair (vector field, foliation). As a result, we establish a dynamic interpretation and a generalization of the Levi-Civita connection and Riemannian curvature treated as invariants of the geodesic flow on the tangent bundle.

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References

  1. A. A. Agrachev and R. V. Gamkrelidze, “Symplectic methods in optimization and control,” in: Geometry of Feedback and Optimal Control, Marcel Dekker (1998), pp. 19–77.

  2. A. A. Agrachev and R. V. Gamkrelidze, “Feedback-invariant optimal control theory and diferential geometry-I. Regular extremals,” J. Dyn. Contr. Syst., 3, No. 3, 343–389 (1997).

    MathSciNet  Google Scholar 

  3. A. A. Agrachev, “Feedback-invariant optimal control theory and diferential geometry-I. Jacobi curves for singular extremals,” J. Dyn. Contr. Syst., 4, 583–604 (1998).

    MATH  MathSciNet  Google Scholar 

  4. A. A. Agrachev and I. Zelenko, “Geometry of Jacobi curves, I, II,” J. Dyn. Contr. Syst., 8, 93–140, 167–215 (2002).

    MathSciNet  Google Scholar 

  5. V. I. Arnold and A. B. Givental, “Symplectic geometry,” in: Progress in Science and Technology, Series on Contemprorary Problems in Mathematics, Fundamental Direction [in Russian], 4, All-Union Institute for Scientific and Technical Information, USSR Acad. of Sciences, Moscow (1985), pp. 1–136.

    Google Scholar 

  6. J. W. Milnor and J. D. Stasheff, Characteristic Classes, Princeton Univ. Press (1974).

  7. I. Zelenko, “Variational approach to differential invariants of rank 2 vector distributions,” J. Diff. Geometry Appl. (in press).

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 21, Geometric Problems in Control Theory, 2004.

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Agrachev, A.A., Gamkrelidze, R.V. Vector fields on n-foliated 2n-dimensional manifolds. J Math Sci 135, 3093–3108 (2006). https://doi.org/10.1007/s10958-006-0147-1

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  • DOI: https://doi.org/10.1007/s10958-006-0147-1

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