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Flattening properties of diffeomorphisms of the second-order tangent bundles induced by holomorphically projective diffeomorphisms of Kählerian spaces

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We study the flattening properties of diffeomorphisms of the second-order tangent bundles induced by holomorphically projective diffeomorphisms of Kählerian spaces.

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References

  1. A. V. Aminova, “The groups of transformations of Riemannian manifolds,” in: Totals of Science and Technique. Problems of Geometry [in Russian], VINITI, Moscow (1990), pp. 97–166.

  2. B. A. Dubrovin, A. T. Fomenko, and S. P. Novikov, Modern Geometry – Methods and Applications, Springer, Berlin (1984–1985), Parts 1–3.

  3. K. M. Zubrilin, “p -geodesic diffeomorphisms of tangent bundles induced by holomorphically projective diffeomorphisms of Kahlerian spaces,” Probl. Topol. Sumizh. Pyt., 3, No. 3, 132–162 (2006).

    MATH  Google Scholar 

  4. K. M. Zubrilin, “p -geodesic diffeomorphisms of tangent bundles with connection of a horizontal lift induced by geodesic (projective) diffeomorphisms of bases,” Prikl. Probl. Mekh. Mat., Issue 6, 48–60 (2008).

    Google Scholar 

  5. K. M. Zubrilin, “p -geodesic transformations and their groups in second-order tangent bundles induced by oncircular transformations of bases,” Ukr. Mat. Zh., 61, No. 3, 346–364 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Zulanke and P. Wintgen, Differentialgeometrie und Faserbündel, Wissehschaften, Berlin (1972).

  7. S. G. Leiko, “Linear p -geodesic diffeomorphisms of tangent bundles of higher orders and higher degrees,” Trudy Geom. Semin. (Kazan), Issue 14, 34–46 (1982).

  8. S. G. Leiko, Riemannian Geometry: Manual [in Ukrainian], Astroprint, Odessa (2000).

  9. S. G. Leiko, “p -geodesic transformations and their groups in tangent bundles induced by geodesic transformations of the basic manifold,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 2, 62–71 (1992).

  10. S. G. Leiko, “p -geodesic transformations and their groups in tangent bundles induced by concircular transformations of the basic manifold,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 6, 35–45 (1998).

  11. S. G. Leiko, “p -geodesic sections of a tangent bundle “ Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 3, 32–42 (1994).

  12. V. A. Piliposan, “On a geodesic mapping of tangent bundles,” Trudy Geom. Semin. (Kazan), Issue 18, 57–69 (1988).

    Google Scholar 

  13. V. A. Piliposan, “On a geodesic mapping of tangent bundles of the Riemannian manifolds with the metric of a complete lift (TM, g C) ,” Trudy Geom. Semin. (Kazan), Issue 18, 69–89 (1988).

  14. V. G. Podol’skii, “Infinitesimal motion in a tangent bundle with the metric of a complete lift and the Sasaki metric,” in: Abstracts of the Sixth All-Union Geom. Conf. on Modern Problems of Geometry [in Russian], Vilnius (1975), pp. 189–190.

  15. P. K. Raschewski, Riemannsche Geometrie und Tensoranalysis, Wissenschaft, Frankfurt am Main (1959).

  16. N. S. Sinyukov, Geodesic Mappings of Riemannian Spaces [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  17. A. S. Solodovnikov, “Projective transformations of Riemannian spaces,” Usp. Mat. Nauk, 11, Issue 4 (70), 45–116 (1956).

    MathSciNet  MATH  Google Scholar 

  18. A. P. Shirokov, “The geometry of tangent bundles and spaces over algebras,” in: Totals of Science and Technique. Problems of Geometry [in Russian], VINITI, Moscow (1981), pp. 61–95.

  19. A. P. Shirokov, “On holomorphically projective transformations in a tangent bundle,” Trudy Geom. Semin. (Kazan), Issue 11, 111–114 (1979).

    Google Scholar 

  20. L. P. Eisenhart, Continuous Groups of Transformations, Dover, New York (1961).

    MATH  Google Scholar 

  21. S. Ishihara, “Holomorphically projective changes and their group in an almost complex manifold,” Tohoku Math. J., 9, No. 3, 273–297 (1957).

    Article  MathSciNet  MATH  Google Scholar 

  22. T. Otsuki and Y. Tashiro, “On curves in Kahlerian spaces,” Math. J. Okayama Univ., 4, No. 1, 57–78 (1954).

    MathSciNet  MATH  Google Scholar 

  23. R. C. Srivastava, “Generalized geodesics in a Riemannian space,” Bull. Cl. Sci. Acad. Roy. Belg., 5, No. 1, 40–46 (1967).

    Google Scholar 

  24. R. C. Srivastava and K. D. Singh, “ R -geodesics and R -asymptotic lines,” Ann. Polonici Mat., 26, 165–173 (1972).

    MathSciNet  MATH  Google Scholar 

  25. S. Tachibana and S. Ishihara, “On infinitesimal holomorphically projective transformations in Kahlerian manifolds,” Tohoku Math. J., 12, No. 1, 77–101 (1960).

    Article  MathSciNet  MATH  Google Scholar 

  26. Y. Tashiro, “On holomorphically projective correspondences in an almost complex space,” Math. J. Okayama Univ., 6, No. 2, 147–152 (1957).

    MathSciNet  MATH  Google Scholar 

  27. K. Yano, “Concircular geometry. I–IV,” in: Proc. Imp. Acad. Tokyo, 16, 195–200; 354–360; 442–448; 505–511 (1940).

  28. K. Yano and S. Ishihara, Tangent and Cotangent Bundles. Differential Geometry, Marcel Dekker, New York (1973).

    MATH  Google Scholar 

  29. K. Yano and S. Ishihara, “Differential geometry of tangent bundles of order 2,” Kodai Math. Semin. Rep., 20, No. 3, 318–354 (1968).

    Article  MathSciNet  MATH  Google Scholar 

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 54, No. 4, pp. 20–35, October–December, 2011.

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Zubrilin, K.M. Flattening properties of diffeomorphisms of the second-order tangent bundles induced by holomorphically projective diffeomorphisms of Kählerian spaces. J Math Sci 187, 550–573 (2012). https://doi.org/10.1007/s10958-012-1083-x

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