参考文献:1. R. C. Srivastava, “Generalized Geodesics in a Riemannian Space,-Bull. Cl. Sci., 5e Sér., Acad. Roy. Belg. 53(1), 40-6 (1967). 2. R. C. Srivastava and K. D. Singh, -em class="a-plus-plus">R-Geodesics and / R-Asymptotic Lines,-Ann. Polonici mat. 26, 165-73 (1972). 3. P. K. Rashevskii, / Riemannian Geometry and Tensor Calculus (Nauka, Moscow, 1967) [in Russian]. 4. T. Otsuki and Y. Tashiro, “On Curves in Kahlerian Spaces,-Math. J. Okayama Univ. 4(1), 57-8 (1954). 5. N. S. Sinyukov, / GeodesicMappings of Riemannian Spaces (Nauka, Moscow, 1979) [in Russian]. 6. Y. Tashiro, “On Holomorphically Projective Correspondences in an Almost Complex Space,-Math. J. Okayama Univ. 6(2), 147-52 (1957). 7. K. Yano, “Concircular Geometry I–IV,-Proc. Imp. Acad. Tokyo 16, 195-00, 354-60, 442-48, 505-11 (1940). CrossRef 8. S. G. Leiko, “Linear / p-Geodesic Diffeomorphisms of Tangent Bundles of Higher Orders and Higher Degrees,-Trudy Geometrich. semin. (Kazan University, Kazan, 1982), No. 14, pp. 34-6. 9. S. G. Leiko, -em class="a-plus-plus">p-Geodesic Transformations of the Tangent Bundles, Induced by Geodesic Transformations of Base Manifolds,-Izv. Vyssh. Uchebn. Zaved. Mat., No. 2, 62-1 (1992) [Russian Mathematics (Iz. VUZ) 36 (2), 62-1 (1992)]. 10. S.G. Leiko, “The / P-Geodesic Transformations of Tangent Bundles, Induced by Concircular Transformations of Base Manifold, and Their Groups,-Izv. Vyssh. Uchebn. Zaved. Mat., No. 6, 35-5 (1998) [Russian Mathematics (Iz. VUZ) 42 (6), 32-1 (1998)]. 11. S. G. Leiko, -em class="a-plus-plus">p-Geodesic Sections of Tangent Bundle,-Izv. Vyssh. Uchebn. Zaved. Mat., No. 3, 32-2 (1994) [Russian Mathematics (Iz. VUZ) 38 (3), 29-9 (1994)]. 12. S. Tachibana and S. Ishihara, “On Infinitesimal Holomorphically Projective Transformations in K?hlerian Manifolds,-Tohoku Math. J. 12(1), 77-01 (1960). CrossRef 13. A. V. Aminova, “Transformation Groups of Riemannian Manifolds,-Itogi Nauki i Tekhniki, VINITI 22, 97-66 (1990). 14. S. Ishihara, “Holomorphically Projective Changes and Their Groups in an Almost Complex Manifold,-Tohoku Math. J. 9(3), 273-97 (1957). CrossRef 15. A. S. Solodovnikov, “Projective Transformations of Riemannian Spaces,-Usp. Mat. Nauk 11(4), 45-16 (1956). 16. K. Yano and S. Ishihara, / Tangent and Cotangent Bundles. Differential geometry (Marcel Dekker, New York, 1973). 17. K. Yano and S. Ishihara, “Differential Geometry of Tangent Bundles of Order 2,-Kodai Math. Semin. Repts. 20(3), 318-54 (1968). CrossRef 18. K. M. Zubrilin, -em class="a-plus-plus">p-Geodesic Diffeomorphisms of Tangent Bundles Induced by Holomorpically Projective Diffeomorpisms of K?hler Spaces,-Zbirnik Prats Inst. Matem. NAN Ukraini 3(3), 132-62 (2006).
作者单位:K. M. Zubrilin (1)
1. Feodosiya Polytechnical Institute of National University of Shipbuilding, ul. Sovetskaya 19, Feodosiya, Crimea, 98176, Ukraine
ISSN:1934-810X
文摘
We study the flattening properties of the infinitesimal transformations of the tangent bundle of a K?hler space generated by lifts of vector fields generating infinitesimal holomorphically projective transformations.