| Title:
|
Reflections with respect to submanifolds in contact geometry (English) |
| Author:
|
Bueken, P. |
| Author:
|
Vanhecke, Lieven |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
29 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
43-57 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
almost contact metric manifolds |
| Keyword:
|
submanifolds |
| Keyword:
|
reflections |
| MSC:
|
53C15 |
| MSC:
|
53C25 |
| MSC:
|
53C40 |
| idZBL:
|
Zbl 0810.53022 |
| idMR:
|
MR1242628 |
| . |
| Date available:
|
2008-06-06T21:23:48Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107466 |
| . |
| Reference:
|
[1] Blair, D. E.: Contact manifolds in Riemannian geometry.Lecture Notes in Mathematics 509 (1976), Springer-Verlag, Berlin-Heidelberg-New York. Zbl 0319.53026, MR 0467588 |
| Reference:
|
[2] Bueken, P. , Vanhecke, L.: Geometry and symmetry on Sasakian manifolds.Tsukuba Math. J. 12 (1988), 403-422. MR 0968200 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[5] Bueken, P.: Reflections and rotations in contact geometry.doctoral dissertation, Catholic University Leuven, 1992. |
| Reference:
|
[6] Chen, B. Y., Vanhecke, L.: Isometric, holomorphic and symplectic reflections.Geometriae Dedicata 29 (1989), 259-277. MR 0995302 |
| Reference:
|
[7] Gray, A.: Vector cross products on manifolds.Trans. Amer. Math. Soc. 141 (1969), 465-504. Zbl 0182.24603, MR 0243469 |
| Reference:
|
[8] Kobayashi, S., Nomizu, K.: Foundations of differential geometry I, II.Interscience, New York, 1963 and 1969. MR 0152974 |
| Reference:
|
[9] Sasaki, S.: Almost contact manifolds I, II, III.Lecture Notes (1965, 1967 and 1968), Mathematical Institute, Tôhoku University. MR 0215232 |
| Reference:
|
[10] Sekigawa, K.: Almost complex submanifolds of a six-dimensional sphere.Kodai Math. J. 6 (1983), 174-185. MR 0702939 |
| Reference:
|
[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 |
| Reference:
|
[12] Tondeur, Ph., Vanhecke L.: Reflections in submanifolds.Geometriae Dedicata 28 (1988), 77-85. MR 0965832 |
| Reference:
|
[13] Tondeur, Ph., Vanhecke, L.: Isometric reflections with respect to submanifolds.Simon Stevin 63 (1989), 107-116. MR 1025491 |
| Reference:
|
[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 |
| Reference:
|
[15] Yano, K., Kon, M.: Structures on manifolds.Series in Pure Mathematics 3 (1984), World Scientific Publ. Co., Singapore. MR 0794310 |
| Reference:
|
[16] Yano, K., Kon, M.: CR submanifolds of Kaehlerian and Sasakian manifolds.Progress in Mathematics 30 (1983), Birkhäuser, Boston, Basel, Stuttgart. MR 0688816 |
| . |
