Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-20T00:58:48.094Z Has data issue: false hasContentIssue false
  • English
  • Français

Vector Fields and Infinitesimal Transformations on Almost-Hermitian Manifolds with Boundary

Published online by Cambridge University Press:  20 November 2018

Arthur L. Hilt  and
Chuan-Chih Hsiung
Arthur L. Hilt
Affiliation:
General Electric Company and Lehigh University
Chuan-Chih Hsiung
Affiliation:
General Electric Company and Lehigh University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Many authors have made interesting and important contributions to the study of vector fields or infinitesimal transformations on compact orientable Riemannian manifolds and Hermitian manifolds without boundary. Recently, Hsiung (6, 7, 8) has extended some of these results to compact orientable Riemannian manifolds with boundary. The purpose of this paper is to continue Hsiung's work by studying vector fields and infinitesimal transformations on almost-Hermitian manifolds with boundary.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 213 - 238
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Apte, M., Sur les isométries des variétés presque kdhlertenues, C. R. Acad. Sci. Paris, 242 (1956), 63–65.Google Scholar
2. Cartan, H., Notions d'algèbre différentielle; application aux groupes de Lie et aux variétés où opère un groupe de Lie, Colloque de Topologie (Bruxelles, 1950), pp. 15-27.Google Scholar
3. Eisenhart, L. P., Riemannian geometry (Princeton, 1949).Google Scholar
4. Goldberg, S. I., Conformai transformations of Kdhler manifolds, Bull. Amer. Math. Soc, 66 (1960), 54–58.Google Scholar
5. Goldberg, S. I., Groups of transformations of Kàhler and almost-Kàhler manifolds, Comment. Math. Helv., 35 (1961), 35–46.Google Scholar
6. Hsiung, C. C., Curvature and Betti numbers of compact Riemannian manifolds with boundary, Univ. e Politec. Torino. Rend. Sem. Mat., 17 (1957-58), 95–131.Google Scholar
7. Hsiung, C. C., A note of correction, Univ. e Politec. Torino. Rend. Sem. Mat., 21 (1961-62), 127–129.Google Scholar
8. Hsiung, C. C., Vector fields and infinitesimal transformations on Riemannian manifolds with boundary, to appear.Google Scholar
9. Lichnerowicz, A., Géométrie des groupes de transformations (Paris, 1958).Google Scholar
10. Lichnerowicz, A. Transformations analytiques d'une variété kählerienne compacte, Bull. Math. Soc. Sci. Math. Phys. R. P. Roumaine (N.S.), 2 (50), (1958), 165–174.Google Scholar
11. Sasaki, S. and Yano, K., Pseudo-analytic vectors on pseudo-Kdhlerian manifolds, Pacific J. Math., 5 (1955), 987–993.Google Scholar
12. Tachibana, S., On almost-analytic vectors in almost-Kdhlerian manifolds, Töhoku Math. J., 11 (1959), 247–265.Google Scholar
13. Yano, K., The theory of Lie derivatives and its applications (Amsterdam, 1957).Google Scholar
14. Yano, K., Conformai transformations in Riemannian and Hermitian spaces, Bull. Amer. Math. Soc, 66 (1960), 369–372.Google Scholar
15. Yano, K. and Nagano, T., On geodesic vector fields in a compact orientable Riemannian space, Comment. Math. Helv., 35 (1961), 55–64.Google Scholar