Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
almost contact metric manifolds; submanifolds; reflections
almost contact metric manifolds; submanifolds; reflections
Summary:
We study to what extent some structure-preserving properties of the geodesic reflection with respect to a submanifold of an almost contact manifold influence the geometry of the submanifold and of the ambient space.
References:
[1] Blair, D. E.: Contact manifolds in Riemannian geometry. Lecture Notes in Mathematics 509 (1976), Springer-Verlag, Berlin-Heidelberg-New York. MR 0467588 | Zbl 0319.53026
[2] Bueken, P. , Vanhecke, L.: Geometry and symmetry on Sasakian manifolds. Tsukuba Math. J. 12 (1988), 403-422. MR 0968200
[3] Bueken, P., Vanhecke, L.: Isometric reflections on Sasakian space forms. Proc. VIth Intern. Coll. Differential Geometry 61 (1989), Santiago de Compostela 1988, Cursos y Congresos, Univ. Santiago de Compostela, 51-59. MR 1040835
[4] Bueken, P., Vanhecke, L.: Reflections in contact geometry. Proc. Curvature Geometry Workshop, Lancaster 1989, (Ed. C. T. J. Dodson) (1989), Univ. Lancaster, 175-190. MR 1089892
[5] Bueken, P.: Reflections and rotations in contact geometry. doctoral dissertation, Catholic University Leuven, 1992.
[6] Chen, B. Y., Vanhecke, L.: Isometric, holomorphic and symplectic reflections. Geometriae Dedicata 29 (1989), 259-277. MR 0995302
[7] Gray, A.: Vector cross products on manifolds. Trans. Amer. Math. Soc. 141 (1969), 465-504. MR 0243469 | Zbl 0182.24603
[8] Kobayashi, S., Nomizu, K.: Foundations of differential geometry I, II. Interscience, New York, 1963 and 1969. MR 0152974
[9] Sasaki, S.: Almost contact manifolds I, II, III. Lecture Notes (1965, 1967 and 1968), Mathematical Institute, Tôhoku University. MR 0215232
[10] Sekigawa, K.: Almost complex submanifolds of a six-dimensional sphere. Kodai Math. J. 6 (1983), 174-185. MR 0702939
[11] Tanno, S.: Some transformations on manifolds with almost contact and contact metric structures I,II. Tôhoku Math. J. 15 (1963), 140-147 and 322–331. MR 0150716
[12] Tondeur, Ph., Vanhecke L.: Reflections in submanifolds. Geometriae Dedicata 28 (1988), 77-85. MR 0965832
[13] Tondeur, Ph., Vanhecke, L.: Isometric reflections with respect to submanifolds. Simon Stevin 63 (1989), 107-116. MR 1025491
[14] Vanhecke, L.: Geometry in normal and tubular neighborhoods. Proc. Workshop on Differential Geometry and Topology, Cala Gonone (Sardinia), Rend. Sem. Fac. Sci. Univ. Cagliari Supplemento al Vol. 58 (1988), 73-176. MR 1122858
[15] Yano, K., Kon, M.: Structures on manifolds. Series in Pure Mathematics 3 (1984), World Scientific Publ. Co., Singapore. MR 0794310
[16] Yano, K., Kon, M.: CR submanifolds of Kaehlerian and Sasakian manifolds. Progress in Mathematics 30 (1983), Birkhäuser, Boston, Basel, Stuttgart. MR 0688816
Search
Partner of
