Abstract
We study the flattening properties of the infinitesimal transformations of the tangent bundle of a Kähler space generated by lifts of vector fields generating infinitesimal holomorphically projective transformations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. C. Srivastava, “Generalized Geodesics in a Riemannian Space,” Bull. Cl. Sci., 5e Sér., Acad. Roy. Belg. 53(1), 40–46 (1967).
R. C. Srivastava and K. D. Singh, “R-Geodesics and R-Asymptotic Lines,” Ann. Polonici mat. 26, 165–173 (1972).
P. K. Rashevskii, Riemannian Geometry and Tensor Calculus (Nauka, Moscow, 1967) [in Russian].
T. Otsuki and Y. Tashiro, “On Curves in Kahlerian Spaces,” Math. J. Okayama Univ. 4(1), 57–78 (1954).
N. S. Sinyukov, GeodesicMappings of Riemannian Spaces (Nauka, Moscow, 1979) [in Russian].
Y. Tashiro, “On Holomorphically Projective Correspondences in an Almost Complex Space,” Math. J. Okayama Univ. 6(2), 147–152 (1957).
K. Yano, “Concircular Geometry I–IV,” Proc. Imp. Acad. Tokyo 16, 195–200, 354–360, 442–448, 505–511 (1940).
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. 34–46.
S. G. Leiko, “p-Geodesic Transformations of the Tangent Bundles, Induced by Geodesic Transformations of Base Manifolds,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 2, 62–71 (1992) [Russian Mathematics (Iz. VUZ) 36 (2), 62–71 (1992)].
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, 35–45 (1998) [Russian Mathematics (Iz. VUZ) 42 (6), 32–41 (1998)].
S. G. Leiko, “p-Geodesic Sections of Tangent Bundle,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 3, 32–42 (1994) [Russian Mathematics (Iz. VUZ) 38 (3), 29–39 (1994)].
S. Tachibana and S. Ishihara, “On Infinitesimal Holomorphically Projective Transformations in Kählerian Manifolds,” Tohoku Math. J. 12(1), 77–101 (1960).
A. V. Aminova, “Transformation Groups of Riemannian Manifolds,” Itogi Nauki i Tekhniki, VINITI 22, 97–166 (1990).
S. Ishihara, “Holomorphically Projective Changes and Their Groups in an Almost Complex Manifold,” Tohoku Math. J. 9(3), 273–297 (1957).
A. S. Solodovnikov, “Projective Transformations of Riemannian Spaces,” Usp. Mat. Nauk 11(4), 45–116 (1956).
K. Yano and S. Ishihara, Tangent and Cotangent Bundles. Differential geometry (Marcel Dekker, New York, 1973).
K. Yano and S. Ishihara, “Differential Geometry of Tangent Bundles of Order 2,” Kodai Math. Semin. Repts. 20(3), 318–354 (1968).
K. M. Zubrilin, “p-Geodesic Diffeomorphisms of Tangent Bundles Induced by Holomorpically Projective Diffeomorpisms of Kähler Spaces,” Zbirnik Prats Inst. Matem. NAN Ukraini 3(3), 132–162 (2006).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © K.M. Zubrilin, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 11, pp. 36–50.
About this article
Cite this article
Zubrilin, K.M. p-geodesic transformations induced by infinitesimal holomorphically projective transformations of Kähler spaces. Russ Math. 56, 31–44 (2012). https://doi.org/10.3103/S1066369X12110035
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X12110035